Celebratio Mathematica

Benedict H. Gross

Complete Bibliography

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B. H. Gross: “In­ter­sec­tion tri­angles and block in­ter­sec­tion num­bers of Stein­er sys­tems,” Math. Z. 139 (June 1974), pp. 87–​104. MR 357146 Zbl 0276.​05018 article

B. H. Gross: Arith­met­ic on el­lipt­ic curves with com­plex mul­ti­plic­a­tion. Ph.D. thesis, Har­vard Uni­versity, 1978. Ad­vised by J. Tate, Jr. A ver­sion of this was pub­lished in two parts: part I as a mono­graph in 1980; part II in In­vent. Math. 79 (1985). MR 2940819 phdthesis

B. H. Gross: “On the peri­ods of abeli­an in­teg­rals and a for­mula of Chow­la and Sel­berg,” In­vent. Math. 45 : 2 (1978), pp. 193–​211. With an ap­pendix by Dav­id E. Rohr­lich. MR 480542 Zbl 0418.​14023 article

B. H. Gross and D. E. Rohr­lich: “Some res­ults on the Mor­dell–Weil group of the Jac­obi­an of the Fer­mat curve,” In­vent. Math. 44 : 3 (1978), pp. 201–​224. MR 491708 Zbl 0369.​14011 article

B. H. Gross and N. Kob­litz: “Gauss sums and the \( p \)-ad­ic \( \Gamma \)-func­tion,” Ann. Math. (2) 109 : 3 (May 1979), pp. 569–​581. MR 534763 Zbl 0406.​12010 article

B. H. Gross: “On an iden­tity of Chow­la and Sel­berg,” pp. 344–​348 in S. Chow­la an­niversary is­sue, published as J. Num­ber The­ory 11 : 3. Issue edi­ted by R. P. Bam­bah. Aca­dem­ic Press (San Diego, CA), August 1979. MR 544262 Zbl 0418.​14024 incollection

B. H. Gross: “Rami­fic­a­tion in \( p \)-ad­ic Lie ex­ten­sions,” pp. 81–​102 in Journées de géométrie algébrique de Rennes: Groupes formels, re­présen­t­a­tions galois­i­ennes et co­homo­lo­gie des variétés de ca­ra­ctéristique pos­it­ive, III [Al­geb­ra­ic geo­metry pro­ceed­ings from Rennes: Form­al groups, Galois rep­res­ent­a­tions and the co­homo­logy of vari­et­ies of pos­it­ive char­ac­ter­ist­ic, III] (Rennes, France, Ju­ly 1978). Edi­ted by P. Ber­th­el­ot and L. Breen. Astérisque 65. Société Mathématique de France (Par­is), 1979. MR 563473 Zbl 0423.​14030 incollection

B. H. Gross: Arith­met­ic on el­lipt­ic curves with com­plex mul­ti­plic­a­tion. Lec­ture Notes in Math­em­at­ics 776. Spring­er (Cham, Switzer­land), 1980. With an ap­pendix by B. Mazur. MR 563921 Zbl 0433.​14032 book

B. H. Gross: “On the fac­tor­iz­a­tion of \( p \)-ad­ic \( L \)-series,” In­vent. Math. 57 : 1 (1980), pp. 83–​95. MR 564185 Zbl 0472.​12011 article

B. H. Gross and D. Za­gi­er: “On the crit­ic­al val­ues of Hecke \( L \)-series,” Mém. Soc. Math. France (N.S.) 2 (1980), pp. 49–​54. MR 608638 Zbl 0462.​14015 article

L. J. Fe­der­er and B. H. Gross: “Reg­u­lat­ors and Iwas­awa mod­ules,” In­vent. Math. 62 : 3 (1981), pp. 443–​457. With an ap­pendix by War­ren Sin­nott. MR 604838 Zbl 0468.​12005 article

B. H. Gross and J. Har­ris: “Real al­geb­ra­ic curves,” Ann. Sci. École Norm. Sup. (4) 14 : 2 (1981), pp. 157–​182. MR 631748 Zbl 0533.​14011 article

B. H. Gross: “\( p \)-ad­ic \( L \)-series at \( s = 0 \),” J. Fac. Sci. Univ. Tokyo Sect. IA Math. 28 : 3 (1981), pp. 979–​994. To the memory of Tak­uro Shintani. MR 656068 Zbl 0507.​12010 article

B. H. Gross: “The an­ni­hil­a­tion of di­visor classes in Abeli­an ex­ten­sions of the ra­tion­al func­tion field” in Sémin­aire de Théorie des Nombres, 1981–1982 (Bor­deaux, France, 1980–1981). Edi­ted by M. J. Bertin. Sémin­aire de Théorie des Nombres, Uni­versité Bor­deaux I. Uni­versité Bor­deaux, 1981. Ex­posé no. 3, 5 pages. Zbl 0507.​14020 incollection

B. H. Gross: “To­po­lo­gic­al in­vari­ants of real al­geb­ra­ic curves” (Gren­oble, France, Janu­ary 1981). Sémin­aire de Théorie des Nombres de Gren­oble 9: 1980–​1981. Uni­versité Sci­en­ti­fique et Médicale de Gren­oble, 1981. Ex­posé no. 2, 2 pages. Zbl 0508.​14022 incollection

B. H. Gross: “Al­geb­ra­ic Hecke char­ac­ters for func­tion fields,” pp. 87–​90 in The­or­ie des nombres: Sem­in­aire Delange–Pisot–Poit­ou (Par­is, 1980–1981). Pro­gress in Math­em­at­ics 22. Birkhäuser (Cham, Switzer­land), 1982. MR 693312 Zbl 0512.​12012 incollection

B. H. Gross: “Hee­gn­er points on \( X_0(11) \)” in Sémin­aire de Théorie des Nombres, 1981–1982 (Bor­deaux, France, 1981–1982). Edi­ted by M. J. Bertin. Sémin­aire de Théorie des Nombres, Uni­versité Bor­deaux I. Uni­versité Bor­deaux, 1982. Ex­posé no. 34, 5 pages. MR 695347 Zbl 0514.​14017 incollection

B. H. Gross: “Min­im­al mod­els for el­lipt­ic curves with com­plex mul­ti­plic­a­tion,” Com­posi­tio Math. 45 : 2 (1982), pp. 155–​164. MR 651979 Zbl 0541.​14010 article

B. H. Gross: “On the con­jec­ture of Birch and Swin­ner­ton-Dyer for el­lipt­ic curves with com­plex mul­ti­plic­a­tion,” pp. 219–​236 in Num­ber the­ory re­lated to Fer­mat’s last the­or­em: Pro­ceed­ings of the con­fer­ence sponsored by the Vaughn Found­a­tion (Cam­bridge, MA, Septem­ber 1981). Edi­ted by N. Kob­litz. Pro­gress in Math­em­at­ics 26. Birkhäuser (Bo­ston), 1982. MR 685298 Zbl 0506.​14040 incollection

B. Gross and D. Za­gi­er: “Points de Hee­gn­er et dérivées de fonc­tions \( L \)” [Hee­gn­er points and de­riv­at­ives of \( L \)-func­tions], C. R. Acad. Sci., Par­is, Sér. I 297 (1983), pp. 85–​87. With Eng­lish sum­mary. An ex­pan­ded ver­sion of this was pub­lished in In­vent. Math. 84 (1986). MR 720914 Zbl 0538.​14023 article

B. H. Gross: “Hee­gn­er points on \( X_0(N) \),” pp. 87–​105 in Mod­u­lar forms: Con­tri­bu­tions to a sym­posi­um on mod­u­lar forms of one and sev­er­al vari­ables (Durham, UK, 30 June–10 Ju­ly 1983). Edi­ted by R. A. Rankin. El­lis Hor­wood Series in Math­em­at­ics and its Ap­plic­a­tions. El­lis Hor­wood Lim­ited (Chichester, UK), 1984. MR 803364 Zbl 0559.​14011 incollection

B. H. Gross and D. B. Za­gi­er: “On sin­gu­lar mod­uli,” J. Reine An­gew. Math. 355 (1985), pp. 191–​220. Ded­ic­ated to J.-P. Serre. MR 772491 Zbl 0545.​10015 article

J. P. Buhler and B. H. Gross: “Arith­met­ic on el­lipt­ic curves with com­plex mul­ti­plic­a­tion, II,” In­vent. Math. 79 : 1 (1985), pp. 11–​29. Part I was Gross’s 1980 LNM mono­graph. Both parts ap­pear to be based on his 1978 PhD thes­is. MR 774527 Zbl 0584.​14027 article

J. P. Buhler, B. H. Gross, and D. B. Za­gi­er: “On the con­jec­ture of Birch and Swin­ner­ton-Dyer for an el­lipt­ic curve of \( \operatorname{rank} 3 \),” Math. Com­put. 44 : 170 (April 1985), pp. 473–​481. MR 777279 Zbl 0606.​14021 article

B. H. Gross and J. Lu­b­in: “The Ei­s­en­stein des­cent on \( J_0(N) \),” In­vent. Math. 83 : 2 (June 1986), pp. 303–​319. MR 818355 Zbl 0594.​14027 article

B. H. Gross and D. B. Za­gi­er: “Hee­gn­er points and de­riv­at­ives of \( L \)-series,” In­vent. Math. 84 (1986), pp. 225–​320. To John Tate. This work ex­pands on a short note pub­lished in C. R. Acad. Sci., Par­is 297 (1983). Part II was pub­lished in Math. Ann. 278 (1987). MR 833192 Zbl 0608.​14019 article

B. H. Gross: “On ca­non­ic­al and quasi-ca­non­ic­al lift­ings,” In­vent. Math. 84 : 2 (June 1986), pp. 321–​326. MR 833193 Zbl 0597.​14044 article

B. H. Gross: “Loc­al heights on curves,” pp. 327–​339 in Arith­met­ic geo­metry (Storrs, CT, 30 Ju­ly–10 Au­gust 1984). Edi­ted by G. Cor­nell and J. H. Sil­ver­man. Spring­er (New York), 1986. MR 861983 Zbl 0605.​14027 incollection

B. H. Gross: “Hee­gn­er points and the mod­u­lar curve of prime level,” J. Math. Soc. Ja­pan 39 : 2 (April 1987), pp. 345–​362. MR 879933 Zbl 0623.​14010 article

B. H. Gross: “Rep­res­ent­a­tion the­ory and the cuspid­al group of \( X(p) \),” Duke Math. J. 54 : 1 (1987), pp. 67–​75. To Yu. I. Man­in. MR 885776 Zbl 0629.​14021 article

B. H. Gross: “Heights and the spe­cial val­ues of \( L \)-series,” pp. 115–​187 in Num­ber the­ory (Montreal, 17–29 June 1985). Edi­ted by H. Kisilevsky and J. Lab­ute. CMS Con­fer­ence Pro­ceed­ings 7. Amer­ic­an Math­em­at­ic­al So­ci­ety (Provid­ence, RI), 1987. MR 894322 Zbl 0623.​10019 incollection

B. Gross, W. Kohnen, and D. Za­gi­er: “Hee­gn­er points and de­riv­at­ives of \( L \)-series, II,” Math. Ann. 278 (1987), pp. 497–​562. Part I was pub­lished in In­ven­tiones Math­em­at­icae 84 (1986). MR 909238 Zbl 0641.​14013 article

B. H. Gross: “Heights and \( L \)-series,” pp. 425–​433 in Pro­ceed­ings of the In­ter­na­tion­al Con­gress of Math­em­aticians (Berke­ley, CA, 3–11 Au­gust 1986), vol. 1. Edi­ted by A. M. Gleason. Amer­ic­an Math­em­at­ic­al So­ci­ety (Provid­ence, RI), 1987. MR 934242 Zbl 0665.​14010 incollection

B. H. Gross: “On the val­ues of abeli­an \( L \)-func­tions at \( s = 0 \),” J. Fac. Sci., Univ. Tokyo, Sect. I A 35 : 1 (1988), pp. 177–​197. MR 931448 Zbl 0681.​12005 article

B. Gross and M. Rosen: “Four­i­er series and the spe­cial val­ues of \( L \)-func­tions,” Adv. Math. 69 : 1 (May 1988), pp. 1–​31. MR 937316 Zbl 0649.​12009 article

B. H. Gross: “Loc­al or­ders, root num­bers, and mod­u­lar curves,” Am. J. Math. 110 : 6 (December 1988), pp. 1153–​1182. MR 970123 Zbl 0675.​12011 article

R. F. Cole­man and B. H. Gross: “\( p \)-ad­ic heights on curves,” pp. 73–​81 in Al­geb­ra­ic num­ber the­ory: In hon­or of K. Iwas­awa (Berke­ley, CA, 20–24 Janu­ary 1987). Edi­ted by J. Coates. Ad­vanced Stud­ies in Pure Math­em­at­ics 17. Aca­dem­ic Press (Bo­ston), 1989. MR 1097610 Zbl 0758.​14009 incollection

B. H. Gross: “Group rep­res­ent­a­tions and lat­tices,” J. Am. Math. Soc. 3 : 4 (October 1990), pp. 929–​960. MR 1071117 Zbl 0745.​11035 article

B. H. Gross: “A tame­ness cri­terion for Galois rep­res­ent­a­tions as­so­ci­ated to mod­u­lar forms mod \( p \),” Duke Math. J. 61 : 2 (1990), pp. 445–​517. MR 1074305 Zbl 0743.​11030 article

B. H. Gross: “Some ap­plic­a­tions of Gel’fand pairs to num­ber the­ory,” Bull. Am. Math. Soc., New Ser. 24 : 2 (1991), pp. 277–​301. MR 1074028 Zbl 0733.​11018 article

B. H. Gross: “Kolyva­gin’s work on mod­u­lar el­lipt­ic curves,” pp. 235–​256 in \( L \)-func­tions and arith­met­ic (Durham, UK, 30 June–11 Ju­ly 1989). Edi­ted by J. Coates and M. J. Taylor. Lon­don Math­em­at­ic­al So­ci­ety Lec­ture Note Series 153. Cam­bridge Uni­versity Press, 1991. MR 1110395 Zbl 0743.​14021 incollection

B. H. Gross and D. Prasad: “Test vec­tors for lin­ear forms,” Math. Ann. 291 : 2 (1991), pp. 343–​355. MR 1129372 Zbl 0768.​22004 article

B. H. Gross and S. S. Kudla: “Heights and the cent­ral crit­ic­al val­ues of triple product \( L \)-func­tions,” Com­pos. Math. 81 : 2 (1992), pp. 143–​209. MR 1145805 Zbl 0807.​11027 article

B. H. Gross: “El­lipt­ic curves and mod­u­lar forms,” pp. 85–​88 in Math­em­at­ics in­to the twenty-first cen­tury (Provid­ence, RI, 8–12 Au­gust 1988). Edi­ted by F. E. Browder. Amer­ic­an Math­em­at­ic­al So­ci­ety (Provid­ence, RI), 1992. MR 1184615 Zbl 1011.​11503 incollection

B. H. Gross and D. Prasad: “On the de­com­pos­i­tion of a rep­res­ent­a­tion of \( \mathrm{SO}_n \) when re­stric­ted to \( \mathrm{SO}_{n-1} \),” Can. J. Math. 44 : 5 (1992), pp. 974–​1002. MR 1186476 Zbl 0787.​22018 article

B. H. Gross and K. Keat­ing: “On the in­ter­sec­tion of mod­u­lar cor­res­pond­ences,” In­vent. Math. 112 : 2 (1993), pp. 225–​245. MR 1213101 Zbl 0811.​11026 article

M. J. Hop­kins and B. H. Gross: “The ri­gid ana­lyt­ic peri­od map­ping, Lu­b­in–Tate space, and stable ho­mo­topy the­ory,” Bull. Am. Math. Soc., New Ser. 30 : 1 (1994), pp. 76–​86. MR 1217353 Zbl 0857.​55003 article

B. H. Gross: “A re­mark on tube do­mains,” Math. Res. Lett. 1 : 1 (1994), pp. 1–​9. MR 1258484 Zbl 0873.​32032 article

M. J. Hop­kins and B. H. Gross: “Equivari­ant vec­tor bundles on the Lu­b­in–Tate mod­uli space,” pp. 23–​88 in To­po­logy and rep­res­ent­a­tion the­ory (Evan­ston, IL, 1–5 May 1992). Edi­ted by E. M. Fried­lander and M. E. Ma­howald. Amer­ic­an Math­em­at­ic­al So­ci­ety (Provid­ence, RI), 1994. MR 1263712 Zbl 0807.​14037 incollection

B. H. Gross: “\( L \)-func­tions at the cent­ral crit­ic­al point,” pp. 527–​535 in Motives (Seattle, WA, 20 Ju­ly–2 Au­gust 1991). Edi­ted by J.-P. Serre, S. Klei­man, and U. Jannsen. Amer­ic­an Math­em­at­ic­al So­ci­ety (Provid­ence, RI), 1994. MR 1265543 Zbl 0807.​14015 incollection

B. H. Gross and D. Prasad: “On ir­re­du­cible rep­res­ent­a­tions of \( \mathrm{SO}_{2n+1}\times \mathrm{SO}_{2m} \),” Can. J. Math. 46 : 5 (1994), pp. 930–​950. MR 1295124 Zbl 0829.​22031 article

B. H. Gross and N. R. Wal­lach: “A dis­tin­guished fam­ily of unit­ary rep­res­ent­a­tions for the ex­cep­tion­al groups of real rank \( = 4 \),” pp. 289–​304 in Lie the­ory and geo­metry: In hon­or of Ber­tram Kostant on the oc­ca­sion of his 65th birth­day (Cam­bridge, MA, May 1993). Edi­ted by J.-L. Bryl­in­ski, R. Bryl­in­ski, V. Guille­min, and V. Kac. Birkhäuser (Bo­ston), 1994. MR 1327538 Zbl 0839.​22006 incollection

B. H. Gross and C. Schoen: “The mod­i­fied di­ag­on­al cycle on the triple product of a poin­ted curve,” Ann. Inst. Four­i­er 45 : 3 (1995), pp. 649–​679. MR 1340948 Zbl 0822.​14015 article

B. H. Gross: “Groups over \( \mathbb{Z} \),” In­vent. Math. 124 : 1–​3 (1996), pp. 263–​279. To Re­in­hold Rem­mert. MR 1369418 Zbl 0846.​20049 article

N. D. Elkies and B. H. Gross: “The ex­cep­tion­al cone and the Leech lat­tice,” Int. Math. Res. Not. 1996 : 14 (July 1996), pp. 665–​698. MR 1411589 Zbl 0863.​11027 article

B. H. Gross and N. R. Wal­lach: “On qua­ternion­ic dis­crete series rep­res­ent­a­tions, and their con­tinu­ations,” J. Reine An­gew. Math. 1996 : 481 (1996), pp. 73–​123. MR 1421947 Zbl 0857.​22012 article

B. H. Gross and G. Sav­in: “The dual pair \( \mathrm{PGL}_3 \times \mathrm{G}_2 \),” Can. Math. Bull. 40 : 3 (1997), pp. 376–​384. MR 1464847 Zbl 0881.​22010 article

B. H. Gross: “On the motive of a re­duct­ive group,” In­vent. Math. 130 : 2 (1997), pp. 287–​313. MR 1474159 Zbl 0904.​11014 article

B. H. Gross: “On the motive of \( G \) and the prin­cip­al ho­mo­morph­ism \( \mathrm{SL}_2 \to \hat{G} \),” Asi­an J. Math. 1 : 1 (1997), pp. 208–​213. MR 1480995 Zbl 0942.​20031 article

N. Elkies and B. H. Gross: “Em­bed­dings in­to the in­teg­ral oc­to­nions,” pp. 147–​158 in Olga Taussky-Todd: In me­mori­am, published as Pac. J. Math. 181 : 3. Issue edi­ted by M. Aschbach­er, D. Blasi­us, and D. Ra­makrish­nan. In­ter­na­tion­al Press (Cam­bridge, MA), 1997. MR 1610847 Zbl 0981.​11036 incollection

B. Gross, B. Kostant, P. Ra­mond, and S. Stern­berg: “The Weyl char­ac­ter for­mula, the half-spin rep­res­ent­a­tions, and equal rank sub­groups,” Proc. Natl. Acad. Sci. USA 95 : 15 (July 1998), pp. 8441–​8442. MR 1639139 Zbl 0918.​17002 article

B. H. Gross: “Mod­u­lar forms mod \( p \) and Galois rep­res­ent­a­tions,” Int. Math. Res. Not. 1998 : 16 (1998), pp. 865–​875. MR 1643625 Zbl 0978.​11018 article

B. H. Gross and G. Sav­in: “Motives with Galois group of type \( \mathrm{G}_2 \): An ex­cep­tion­al theta-cor­res­pond­ence,” Com­pos. Math. 114 : 2 (1998), pp. 153–​217. MR 1661756 Zbl 0931.​11015 article

B. H. Gross: “On the Satake iso­morph­ism,” pp. 223–​237 in Galois rep­res­ent­a­tions in arith­met­ic al­geb­ra­ic geo­metry (Durham, UK, 9–18 Ju­ly 1996). Edi­ted by A. J. Scholl and R. L. Taylor. Cam­bridge Uni­versity Press, 1998. MR 1696481 Zbl 0996.​11038 incollection

B. H. Gross and W. T. Gan: “Haar meas­ure and the Artin con­duct­or,” Trans. Am. Math. Soc. 351 : 4 (1999), pp. 1691–​1704. MR 1458303 Zbl 0991.​20033 article

B. H. Gross and W. T. Gan: “Com­mut­at­ive sub­rings of cer­tain non-as­so­ci­at­ive rings,” Math. Ann. 314 : 2 (1999), pp. 265–​283. MR 1697445 Zbl 0990.​11018 article

B. H. Gross: “Al­geb­ra­ic mod­u­lar forms,” Is­rael J. Math. 113 (December 1999), pp. 61–​93. MR 1729443 Zbl 0965.​11020 article

B. H. Gross: “On simply-con­nec­ted groups over \( \mathbf{Z} \), with \( G(\mathbf{R}) \) com­pact,” pp. 113–​118 in In­teg­ral quad­rat­ic forms and lat­tices: Ded­ic­ated to the memory of Den­nis Ray Estes (Seoul, 15–19 June 1998). Edi­ted by M.-H. Kim, J. S. Hsia, Y. Kitaoka, and R. Schulze-Pil­lot. Con­tem­por­ary Math­em­at­ics 249. Amer­ic­an Math­em­at­ic­al So­ci­ety (Provid­ence, RI), 1999. MR 1732354 Zbl 0969.​20023 incollection

B. Gross and N. Wal­lach: “Re­stric­tion of small dis­crete series rep­res­ent­a­tions to sym­met­ric sub­groups,” pp. 255–​272 in The math­em­at­ic­al leg­acy of Har­ish-Chandra: A cel­eb­ra­tion of rep­res­ent­a­tion the­ory and har­mon­ic ana­lys­is (Bal­timore, MD, 9–10 Janu­ary 1998). Edi­ted by R. S. Dor­an and V. S. Varada­ra­jan. Pro­ceed­ings of Sym­po­sia in Pure Math­em­at­ics 68. Amer­ic­an Math­em­at­ic­al So­ci­ety (Provid­ence, RI), 2000. MR 1767899 Zbl 0960.​22008 incollection

W. T. Gan and B. H. Gross: “In­teg­ral em­bed­dings of cu­bic norm struc­tures,” J. Al­gebra 233 : 1 (November 2000), pp. 363–​397. To Nath­an Jac­ob­son, in me­mori­am. MR 1793601 Zbl 0990.​11017 article

B. H. Gross: “On minus­cule rep­res­ent­a­tions and the prin­cip­al \( \mathrm{SL}_2 \),” Rep­res­ent. The­ory 4 (2000), pp. 225–​244. MR 1795753 Zbl 0986.​22011 article

N. D. Elkies and B. H. Gross: “Cu­bic rings and the ex­cep­tion­al Jordan al­gebra,” Duke Math. J. 109 : 2 (2001), pp. 383–​409. MR 1845183 Zbl 1028.​11041 article

W. T. Gan, B. Gross, and G. Sav­in: “Four­i­er coef­fi­cients of mod­u­lar forms on \( G_2 \),” Duke Math. J. 115 : 1 (2002), pp. 105–​169. MR 1932327 Zbl 1165.​11315 article

B. H. Gross and C. T. McMul­len: “Auto­morph­isms of even un­im­od­u­lar lat­tices and un­rami­fied Salem num­bers,” J. Al­gebra 257 : 2 (November 2002), pp. 265–​290. Ded­ic­ated to J. G. Thompson on his 70th birth­day. MR 1947324 Zbl 1022.​11016 article

P. De­ligne and B. H. Gross: “On the ex­cep­tion­al series, and its des­cend­ants,” C. R. Math. Acad. Sci. Par­is 335 : 11 (2002), pp. 877–​881. With French sum­mary. MR 1952563 Zbl 1017.​22008 article

B. H. Gross: “Un­rami­fied re­cip­roc­al poly­no­mi­als and Coxeter de­com­pos­i­tions,” Mo­sc. Math. J. 2 : 4 (October–December 2002), pp. 681–​692. Ded­ic­ated to Yuri I. Man­in on the oc­ca­sion of his 65th birth­day. MR 1986086 Zbl 1136.​11313 article

B. H. Gross: “Some re­marks on signs in func­tion­al equa­tions,” Ramanu­jan J. 7 : 1–​3 (2003), pp. 91–​93. In memory of Robert A. Rankin. MR 2035794 Zbl 1057.​11052 article

B. H. Gross and G. Nebe: “Glob­ally max­im­al arith­met­ic groups,” J. Al­gebra 272 : 2 (February 2004), pp. 625–​642. MR 2028074 Zbl 1113.​20040 article

B. H. Gross and J. Har­ris: “On some geo­met­ric con­struc­tions re­lated to theta char­ac­ter­ist­ics,” pp. 279–​311 in Con­tri­bu­tions to auto­morph­ic forms, geo­metry, and num­ber the­ory: Pa­pers from the con­fer­ence in hon­or of Joseph Sha­lika on the oc­ca­sion of his 60th birth­day (Bal­timore, MD, 14–17 May 2002). Edi­ted by H. Hida, D. Ra­makrish­nan, and F. Shahidi. Johns Hop­kins Uni­versity Press (Bal­timore, MD), 2004. MR 2058611 Zbl 1072.​14032 incollection

B. Birch and B. Gross: “Cor­res­pond­ence,” pp. 11–​23 in Hee­gn­er points and Rankin \( L \)-series (Berke­ley, CA, Decem­ber 2001). Edi­ted by H. Dar­mon and S.-W. Zhang. MSRI Pub­lic­a­tions 49. Cam­bridge Uni­versity Press, 2004. MR 2083208 Zbl 1073.​11002 incollection

B. H. Gross: “Hee­gn­er points and rep­res­ent­a­tion the­ory,” pp. 37–​65 in Hee­gn­er points and Rankin \( L \)-series (Berke­ley, CA, Decem­ber 2001). Edi­ted by H. Dar­mon and S.-W. Zhang. MSRI Pub­lic­a­tions 49. Cam­bridge Uni­versity Press, 2004. MR 2083210 Zbl 1126.​11032 incollection

B. H. Gross and J. Har­ris: The ma­gic of num­bers. Pren­tice Hall (Up­per Saddle River, NJ), 2004. Zbl 1121.​00004 book

B. H. Gross: “An el­lipt­ic curve test for Mersenne primes,” J. Num­ber The­ory 110 : 1 (January 2005), pp. 114–​119. MR 2114676 Zbl 1074.​11065 article

B. H. Gross and D. Pol­lack: “On the Euler char­ac­ter­ist­ic of the dis­crete spec­trum,” J. Num­ber The­ory 110 : 1 (January 2005), pp. 136–​163. MR 2114678 Zbl 1080.​11041 article

B. H. Gross: “On the cent­ral­izer of a reg­u­lar, semi-simple, stable con­jugacy class,” Rep­res­ent. The­ory 9 (2005), pp. 287–​296. MR 2133761 Zbl 1107.​20034 article

A. Pacetti and F. Rodrig­uez Vil­le­g­as: “Com­put­ing weight 2 mod­u­lar forms of level \( p^2 \),” Math. Com­put. 74 : 251 (2005), pp. 1545–​1557. With an ap­pendix by B. Gross. MR 2137017 Zbl 1093.​11027 article

B. H. Gross: “On the val­ues of Artin \( L \)-func­tions,” Q. J. Pure Ap­pl. Math. 1 : 1 (2005), pp. 1–​13. MR 2154331 Zbl 1169.​11050 article

B. H. Gross and M. Reed­er: “From Laplace to Lang­lands via rep­res­ent­a­tions of or­tho­gon­al groups,” Bull. Am. Math. Soc. (N.S.) 43 : 2 (2006), pp. 163–​205. MR 2216109 Zbl 1159.​11047 article

B. H. Gross, E. Hironaka, and C. T. McMul­len: “Cyc­lo­tom­ic factors of Coxeter poly­no­mi­als,” J. Num­ber The­ory 129 : 5 (May 2009), pp. 1034–​1043. MR 2516970 Zbl 1183.​11065 article

B. H. Gross and M. W. Lu­cian­ovic: “On cu­bic rings and qua­ternion rings,” J. Num­ber The­ory 129 : 6 (2009), pp. 1468–​1478. MR 2521487 Zbl 1166.​11034 article

E. Fren­kel and B. Gross: “A ri­gid ir­reg­u­lar con­nec­tion on the pro­ject­ive line,” Ann. Math. (2) 170 : 3 (2009), pp. 1469–​1512. MR 2600880 Zbl 1209.​14017 article

B. H. Gross: “The arith­met­ic of el­lipt­ic curves — an up­date,” Ar­ab. J. Sci. Eng. AS­JE. Math. 34 : 1D (2009), pp. 95–​103. MR 2792223 Zbl 1229.​11088 article

B. H. Gross: “Ri­gid loc­al sys­tems on \( \mathbb{G}_m \) with fi­nite mono­dromy,” Adv. Math. 224 : 6 (August 2010), pp. 2531–​2543. MR 2652215 Zbl 1193.​22001 article

B. H. Gross and M. Reed­er: “Arith­met­ic in­vari­ants of dis­crete Lang­lands para­met­ers,” Duke Math. J. 154 : 3 (September 2010), pp. 431–​508. MR 2730575 Zbl 1207.​11111 article

B. H. Gross: “Ir­re­du­cible cuspid­al rep­res­ent­a­tions with pre­scribed loc­al be­ha­vi­or,” Am. J. Math. 133 : 5 (2011), pp. 1231–​1258. MR 2843098 Zbl 1228.​22017 article

B. H. Gross: “Lec­tures on the con­jec­ture of Birch and Swin­ner­ton-Dyer,” pp. 169–​209 in Arith­met­ic of \( L \)-func­tions (Park City, UT, 28 June–18 Ju­ly 2009). Edi­ted by C. Popes­cu, K. Ru­bin, and A. Sil­ver­berg. IAS/Park City Math­em­at­ics Series 18. Amer­ic­an Math­em­at­ic­al So­ci­ety (Provid­ence, RI), 2011. MR 2882691 Zbl 1285.​11096 incollection

B. H. Gross and N. R. Wal­lach: “On the Hil­bert poly­no­mi­als and Hil­bert series of ho­mo­gen­eous pro­ject­ive vari­et­ies,” pp. 253–​263 in Arith­met­ic geo­metry and auto­morph­ic forms: Fest­s­chrift ded­ic­ated to Steph­en Kudla on the oc­ca­sion of his 60th birth­day. Edi­ted by J. Cog­dell, J. Funke, M. Ra­po­port, and T. Yang. Ad­vanced Lec­tures in Math­em­at­ics 19. In­ter­na­tion­al Press (Somerville, MA), 2011. MR 2906911 Zbl 1310.​14044 incollection

B. H. Gross: “On Bhar­gava’s rep­res­ent­a­tion and Vin­berg’s in­vari­ant the­ory,” pp. 317–​321 in Fron­ti­ers of math­em­at­ic­al sci­ences. Edi­ted by B. Gu and S.-T. Yau. In­ter­na­tion­al Press (Somerville, MA), 2011. MR 3050830 incollection

B. H. Gross and J. A. Par­son: “On the loc­al di­vis­ib­il­ity of Hee­gn­er points,” pp. 215–​241 in Num­ber the­ory, ana­lys­is and geo­metry: In memory of Serge Lang. Edi­ted by D. Gold­feld, J. Jor­gen­son, P. Jones, D. Ra­makrish­nan, K. Ribet, and J. Tate. Spring­er (Ber­lin), 2012. MR 2867919 Zbl 1276.​11091 incollection

B. H. Gross: “The classes of sin­gu­lar mod­uli in the gen­er­al­ized Jac­obi­an,” pp. 137–​141 in Geo­metry and arith­met­ic (Schi­er­mon­nikoog, Neth­er­lands, 20–24 Septem­ber 2010). Edi­ted by C. Faber, G. Far­kas, and R. de Jong. EMS Series of Con­gress Re­ports. European Math­em­at­ic­al So­ci­ety (Zürich), 2012. MR 2987658 Zbl 1317.​11047 incollection

M. Reed­er, P. Levy, J.-K. Yu, and B. H. Gross: “Grad­ings of pos­it­ive rank on simple Lie al­geb­ras,” Trans­form. Groups 17 : 4 (2012), pp. 1123–​1190. MR 3000483 Zbl 1310.​17017 ArXiv 1307.​5765 article

Sur les con­jec­tures de Gross et Prasad, I. Edi­ted by W. T. Gan, B. H. Gross, D. Prasad, and J.-L. Wald­spur­ger. Astérisque 346. Société Mathématique de France (Par­is), 2012. MR 3052279 Zbl 1257.​22001 book

B. H. Gross: “Hanoi lec­tures on the arith­met­ic of hy­per­el­lipt­ic curves,” Acta Math. Vi­et­nam. 37 : 4 (2012), pp. 579–​588. MR 3058664 Zbl 1294.​11107 article

W. T. Gan, B. H. Gross, and D. Prasad: “Sym­plect­ic loc­al root num­bers, cent­ral crit­ic­al \( L \) val­ues, and re­stric­tion prob­lems in the rep­res­ent­a­tion the­ory of clas­sic­al groups,” pp. 1–​109 in Sur les con­jec­tures de Gross et Prasad, I [The con­jec­tures of Gross and Prasad, I]. Edi­ted by W. T. Gan, B. H. Gross, D. Prasad, and J.-L. Wald­spur­ger. Astérisque 346. Société Mathématique de France (Par­is), 2012. MR 3202556 Zbl 1280.​22019 ArXiv 0909.​2999 incollection

W. T. Gan, B. H. Gross, and D. Prasad: “Re­stric­tions of rep­res­ent­a­tions of clas­sic­al groups: Ex­amples,” pp. 111–​170 in Sur les con­jec­tures de Gross et Prasad, I [The con­jec­tures of Gross and Prasad, I]. Edi­ted by W. T. Gan, B. H. Gross, D. Prasad, and J.-L. Wald­spur­ger. Astérisque 346. Société Mathématique de France (Par­is), 2012. with French sum­mary. MR 3202557 Zbl 1279.​22023 ArXiv 0909.​2993 incollection

B. H. Gross: “Trivi­al \( L \)-func­tions for the ra­tion­al func­tion field,” J. Num­ber The­ory 133 : 3 (March 2013), pp. 970–​976. MR 2997780 Zbl 1318.​11147 article

M. Bhar­gava and B. H. Gross: “The av­er­age size of the 2-Selmer group of Jac­obi­ans of hy­per­el­lipt­ic curves hav­ing a ra­tion­al Wei­er­strass point,” pp. 23–​91 in Auto­morph­ic rep­res­ent­a­tions and \( L \)-func­tions (Mum­bai, 3–11 Janu­ary 2012). Edi­ted by D. Prasad, C. S. Ra­jan, A. Sank­aranaray­anan, and J. Sen­gupta. Tata In­sti­tute of Fun­da­ment­al Re­search Stud­ies in Math­em­at­ics 22. Tata In­sti­tute of Fun­da­ment­al Re­search (Mum­bai), 2013. MR 3156850 Zbl 1303.​11072 ArXiv 1208.​1007 incollection

M. Bhar­gava and B. H. Gross: “Arith­met­ic in­vari­ant the­ory,” pp. 33–​54 in Sym­metry: Rep­res­ent­a­tion the­ory and its ap­plic­a­tions. In hon­or of No­lan R. Wal­lach. Edi­ted by R. E. Howe, M. Hun­ziker, and J. F. Wil­len­bring. Pro­gress in Math­em­at­ics 257. Spring­er (Cham, Switzer­land), 2014. Part II was pub­lished in Pro­gress in Math­em­at­ics 312 (2015). MR 3363006 Zbl 1377.​11045 ArXiv 1206.​4774 incollection

B. H. Gross: “The work of Man­jul Bhar­gava,” pp. 56–​63 in Pro­ceed­ings of the In­ter­na­tion­al Con­gress of Math­em­aticians (Seoul, 13–21 Au­gust 2014), vol. 1: Plen­ary lec­tures and ce­re­mon­ies. Edi­ted by S. Y. Jang, Y. R. Kim, D.-W. Lee, and I. Yie. Ky­ung Moon Sa (Seoul), 2014. MR 3728462 Zbl 1373.​11003 incollection

Y. K. Le­ong: “Be­ne­dict Gross: El­lipt­ic curves, Mil­len­ni­um Prob­lem,” published as Im­prints 26 (2015). Re­prin­ted in The art and prac­tice of math­em­at­ics (2021). incollection

M. Bhar­gava, B. H. Gross, and X. Wang: “Arith­met­ic in­vari­ant the­ory, II: Pure in­ner forms and ob­struc­tions to the ex­ist­ence of or­bits,” pp. 139–​171 in Rep­res­ent­a­tions of re­duct­ive groups: In hon­or of the 60th birth­day of Dav­id A. Vogan, Jr. (Cam­bridge, MA, 19–23 May 2014). Edi­ted by M. Nev­ins and P. E. Trapa. Pro­gress in Matem­at­ics 312. Spring­er (Cham, Switzer­land), 2015. Part I was pub­lished in Pro­gress in Math­em­at­ics 257 (2014). MR 3495795 Zbl 1377.​11046 ArXiv 1310.​7689 incollection

B. K. Gross: “On the Lang­lands cor­res­pond­ence for sym­plect­ic motives,” Izv. Ross. Akad. Nauk Ser. Mat. 80 : 4 (2016), pp. 678–​692. Eng­lish trans­la­tion of Rus­si­an ori­gin­al pub­lished in Izv. Ross. Akad. Nauk Ser. Mat. 80:4 (2016). MR 3535358 Zbl 1391.​11075 article

R. Coulangeon, B. H. Gross, and G. Nebe: “Lat­tices and ap­plic­a­tions in num­ber the­ory,” Ober­wolfach Rep. 13 : 1 (2016), pp. 87–​154. Ab­stracts from work­shop held in Ober­wolfach, Ger­many, 17–23 Janu­ary 2016. MR 3586050 Zbl 1380.​00058 article

M. Bhar­gava, B. H. Gross, and X. Wang: “A pos­it­ive pro­por­tion of loc­ally sol­uble hy­per­el­lipt­ic curves over \( \mathbb{Q} \) have no point over any odd de­gree ex­ten­sion,” J. Am. Math. Soc. 30 : 2 (2017), pp. 451–​493. With an ap­pendix by Tim Dokchit­ser and Vladi­mir Dokchit­ser. MR 3600041 Zbl 1385.​11043 ArXiv 1310.​7692 article

B. H. Gross: “On Hecke’s de­com­pos­i­tion of the reg­u­lar dif­fer­en­tials on the mod­u­lar curve of prime level,” Res. Math. Sci. 5 : 1 (2018). Pa­per no. 1, 19 pages. MR 3749283 Zbl 1455.​11083 article

B. Gross, J. Har­ris, and E. Riehl: Fat chance: Prob­ab­il­ity from 0 to 1. Cam­bridge Uni­versity Press, 2019. MR 3931738 Zbl 1423.​00005 book

B. Gross: “A short note on S.-T. Yau,” pp. 46 in Cel­eb­rat­ing Shing-Tung Yau on his 70th birth­day, published as IC­CM Not. 7 : 1. Issue edi­ted by S.-Y. Cheng, L. Ji, and H. X. Xiaok­ui Yang. In­ter­na­tion­al Press (Somerville, MA), 2019. MR 3960553 incollection

J. Achter, F. An­dreatta, L. Bary-Sor­oker, B. Bhatt, P. Cas­sou-Noguès, T. Chin­burg, B. Mor­in, M. J. Taylor, B. Con­rad, C.-L. Chai, H. Esnault, A. Shiho, F. Oort, D. Gross, S. Har­ashita, D. Har­bater, T. Kat­sura, R. Pries, and M. Zieve: “Ap­pendix 3: Ques­tions in arith­met­ic al­geb­ra­ic geo­metry,” pp. 295–​331 in Open prob­lems in arith­met­ic al­geb­ra­ic geo­metry. Edi­ted by F. Oort. Ad­vanced Lec­tures in Math­em­at­ics 46. In­ter­na­tion­al Press (Somerville, MA), 2019. MR 3971189 Zbl 1428.​14005 incollection

B. H. Gross: Simple su­per­cuspid­als and the Lang­lands cor­res­pond­ence. Pre­print, May 2020. ArXiv 2005.​09078 techreport

W. T. Gan, B. H. Gross, and D. Prasad: “Branch­ing laws for clas­sic­al groups: The non-tempered case,” Com­pos. Math. 156 : 11 (2020), pp. 2298–​2367. MR 4190046 Zbl 1470.​11126 ArXiv 1911.​02783 article

B. H. Gross: “On the peri­ods of Abeli­an vari­et­ies,” IC­CM Not. 8 : 2 (2020), pp. 10–​18. MR 4245911 Zbl 1475.​11121 ArXiv 2005.​04194 article

K. Ac­quista, J. Buhler, D. Clausen, J. H. Coates, B. H. Gross, S. Lichten­baum, J. Lu­b­in, B. Mazur, V. K. Murty, B. Per­rin-Ri­ou, C. D. Popes­cu, K. A. Ribet, J. H. Sil­ver­man, K. Uh­len­beck, and J. F. Voloch: “Me­mori­al art­icle for John Tate.” Edi­ted by B. Mazur and K. Ribet. No­tices Am. Math. Soc. 68 : 5 (2021), pp. 768–​781. MR 4249436 Zbl 1470.​01012 article

B. H. Gross and S. Garibaldi: “Minus­cule em­bed­dings,” pp. 987–​1004 in Spe­cial is­sue to the memory of T. A. Spring­er, published as In­d­ag. Math. (N.S.) 32 : 5. Issue edi­ted by G. Cor­ne­lis­sen and E. Op­dam. El­sevi­er (Am­s­ter­dam), September 2021. MR 4310010 Zbl 07394423 incollection

Y. K. Le­ong: “Be­ne­dict Gross: El­lipt­ic curves, Mil­len­ni­um Prob­lem,” pp. 131–​140 in The art and prac­tice of math­em­at­ics: In­ter­views at the In­sti­tute for Math­em­at­ic­al Sci­ences, Na­tion­al Uni­versity of Singa­pore, 2010–2019. World Sci­entif­ic (Singa­pore), 2021. In­ter­view con­duc­ted on 19 March 2012. Ori­gin­ally pub­lished in Im­prints 26 (2015). Zbl 1473.​01034 incollection

B. H. Gross: “In­co­her­ent def­in­ite spaces and Shimura vari­et­ies,” pp. 187–​215 in Re­l­at­ive trace for­mu­las (Schloss El­mau, Ger­many, 22–28 April 2018). Edi­ted by W. Müller, S. W. Shin, and N. Tem­pli­er. Si­mons Sym­po­sia. Spring­er (Cham, Switzer­land), 2021. Zbl 1475.​11124 ArXiv 2005.​05188 incollection

W. T. Gan, B. H. Gross, and D. Prasad: Twis­ted GGP prob­lems and con­jec­tures. Pre­print, April 2022. ArXiv 2204.​10108 techreport