Celebratio Mathematica

Paul T. Bateman

Number theory  ·  UIUC

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P. T. Bate­man: On the rep­res­ent­a­tions of a num­ber as the sum of three squares. Ph.D. thesis, Uni­versity of Pennsylvania, 1946. Ad­vised by H. Rademach­er. An art­icle with this title was pub­lished by Bate­man in 1951. MR 2937758 phdthesis

D. H. Browne, E. P. Starke, P. Bate­man, and M. S. Kne­bel­man: “Prob­lems and solu­tions: Ele­ment­ary prob­lems: Solu­tions: E706,” Amer. Math. Monthly 53 : 9 (1946), pp. 533–​534. MR 1526542 article

R. Du­bisch and P. Bate­man: “Prob­lems and solu­tions: Ele­ment­ary prob­lems: Solu­tions: E718,” Amer. Math. Monthly 53 : 10 (1946), pp. 593. MR 1526565 article

D. H. Browne, P. T. Bate­man, E. P. Starke, and C. D. Olds: “Prob­lems and solu­tions: Solu­tions: E704,” Amer. Math. Monthly 53 : 8 (1946), pp. 467–​468. MR 1526520 article

G. Gross­man and P. Bate­man: “Ele­ment­ary prob­lems and solu­tions: Solu­tions: E719,” Amer. Math. Monthly 54 : 1 (1947), pp. 45–​46. MR 1526591 article

H. Scheffe, P. T. Bate­man, and E. Lat­shaw: “Ele­ment­ary prob­lems and solu­tions: Solu­tions: E734,” Amer. Math. Monthly 54 : 4 (1947), pp. 225–​227. MR 1526678 article

V. Thebault and P. T. Bate­man: “Ad­vanced prob­lems and solu­tions: Solu­tions: 4180,” Amer. Math. Monthly 54 : 3 (1947), pp. 170–​171. MR 1544216 article

V. Thebault and P. Bate­man: “Ad­vanced prob­lems and solu­tions: Solu­tions: 4205,” Amer. Math. Monthly 54 : 9 (1947), pp. 550. MR 1544221 article

E. Szekeres, P. T. Bate­man, and D. K. Pease: “Ele­ment­ary prob­lems and solu­tions: Solu­tions: E740,” Amer. Math. Monthly 54 : 5 (1947), pp. 281–​282. MR 1526700 article

V. Thebault and P. T. Bate­man: “Ele­ment­ary prob­lems and solu­tions: Solu­tions: E745,” Amer. Math. Monthly 54 : 5 (1947), pp. 285. MR 1544144 article

P. T. Bate­man, J. P. Bal­lan­tine, R. Goormaghtigh, H. F. Sand­ham, and V. Thebault: “Ad­vanced prob­lems and solu­tions: Prob­lems for solu­tion: 4290–4294,” Amer. Math. Monthly 55 : 4 (1948), pp. 253–​254. MR 1526955 article

P. T. Bate­man: “Note on the coef­fi­cients of the cyc­lo­tom­ic poly­no­mi­al,” Bull. Am. Math. Soc. 55 : 12 (1949), pp. 1180–​1181. MR 0032677 Zbl 0035.​31102 article

P. T. Bate­man and O. Sza­sz: “Ad­vanced prob­lems and solu­tions: Solu­tions: 4290,” Amer. Math. Monthly 56 : 9 (1949), pp. 639–​640. MR 1527393 article

L. J. Bur­ton, W. Flem­ing, P. D. Thomas, P. T. Bate­man, and J. Rosen­baum: “Ele­ment­ary prob­lems and solu­tions: Prob­lems for solu­tion: E866–E870,” Amer. Math. Monthly 56 : 5 (1949), pp. 338. MR 1527260 article

P. T. Bate­man and S. Chow­la: “Av­er­ages of char­ac­ter sums,” Proc. Am. Math. Soc. 1 : 6 (1950), pp. 781–​787. MR 0042445 Zbl 0041.​01904 article

P. T. Bate­man, S. Chow­la, and P. Er­dős: “Re­marks on the size of \( L(1,\chi) \),” Publ. Math. Debre­cen 1 (1950), pp. 165–​182. MR 0037322 Zbl 0036.​30702 article

P. T. Bate­man: “A re­mark on in­fin­ite groups,” Am. Math. Mon. 57 : 9 (November 1950), pp. 623–​624. MR 0040293 Zbl 0039.​25103 article

P. Un­gar, V. Thebault, P. Bate­man, P. Er­dos, and F. J. Dys­on: “Ad­vanced prob­lems and solu­tions: Prob­lems for solu­tion: 4385–4389,” Amer. Math. Monthly 57 : 3 (1950), pp. 188–​189. MR 1527514 article

P. T. Bate­man and W. H. J. Fuchs: “Ele­ment­ary prob­lems and solu­tions: Solu­tions: E869,” Amer. Math. Monthly 57 : 2 (1950), pp. 114–​116. MR 1527478 article

R. L. Gupta, P. T. Bate­man, P. Er­dos, V. Thebault, and H. F. Sand­ham: “Ad­vanced prob­lems and solu­tions: Prob­lems for solu­tions: 4390–4394,” Amer. Math. Monthly 57 : 4 (1950), pp. 265. MR 1527543 article

P. T. Bate­man: “On the rep­res­ent­a­tions of a num­ber as the sum of three squares,” Trans. Am. Math. Soc. 71 : 1 (1951), pp. 70–​101. This is Bate­man’s 1946 PhD thes­is. MR 0042438 Zbl 0043.​04603 article

P. T. Bate­man: “Book Re­view: Eric H. Neville, ‘The Farey series of or­der 1025, dis­play­ing solu­tions of the di­o­phant­ine equa­tion, \( bx - ay = 1 \),” Bull. Am. Math. Soc. 57 : 4 (1951), pp. 325–​326. MR 1565320 article

P. Bate­man and P. Er­dős: “Geo­met­ric­al ex­trema sug­ges­ted by a lemma of Be­sicov­itch,” Am. Math. Mon. 58 : 5 (May 1951), pp. 306–​314. MR 0041466 Zbl 0043.​16202 article

P. Bate­man: “Ad­vanced prob­lems and solu­tions: Solu­tions: 4387,” Amer. Math. Monthly 58 : 9 (1951), pp. 638–​639. MR 1527985 article

P. T. Bate­man and R. Breusch: “Ad­vanced prob­lems and solu­tions: Solu­tions: 4391,” Amer. Math. Monthly 58 : 10 (1951), pp. 704–​705. MR 1528011 article

N. C. Arkeny, W. Scott, P. T. Bate­man, and L. Schoen­feld: “Ad­vanced prob­lems and solu­tions: Solu­tions: 4421,” Amer. Math. Monthly 59 : 5 (1952), pp. 338. MR 1528162 article

P. T. Bate­man and S. Chow­la: “The equi­val­ence of two con­jec­tures in the the­ory of num­bers,” J. In­di­an Math. Soc. (N.S.) 17 (1953), pp. 177–​181. MR 0062176 Zbl 0055.​27503 article

P. T. Bate­man: “Book Re­view: Har­old Dav­en­port, ‘The high­er arith­met­ic’,” Bull. Am. Math. Soc. 59 : 5 (1953), pp. 473–​474. MR 1565518 article

E. Land­au: Hand­buch der Lehre von der Ver­teilung der Primzah­len, 2nd edition. Chelsea Pub­lish­ing Co. (New York), 1953. In two volumes; with an ap­pendix by Paul T. Bate­man. MR 0068565 book

P. T. Bate­man: “Book Re­view: Har­ald Bo­hr, ‘Col­lec­ted math­em­at­ic­al works’,” Bull. Am. Math. Soc. 60 : 6 (1954), pp. 576–​578. MR 1565624 article

D. J. New­man and P. T. Bate­man: “Ad­vanced prob­lems and solu­tions: Solu­tions: 4459,” Amer. Math. Monthly 61 : 7 (1954), pp. 477–​479. MR 1528794 article

P. T. Bate­man, H. Råd­ström, O. Han­ner, A. M. Mac­beath, C. A. Ro­gers, B. J. Pet­tis, and V. L. Klee: Sem­in­ar on con­vex sets (Prin­ceton, NJ, 1949–1950). In­sti­tute for Ad­vanced Study (Prin­ceton, NJ), 1955. MR 0064421 book

P. T. Bate­man and P. Er­dős: “Par­ti­tions in­to primes,” Publ. Math. Debre­cen 4 (1956), pp. 198–​200. Ded­ic­ated to the memory of Tibor Szele. MR 0079013 Zbl 0073.​03101 article

P. T. Bate­man and P. Er­dős: “Mono­ton­icity of par­ti­tion func­tions,” Math­em­atika 3 : 1 (1956), pp. 1–​14. MR 0080121 Zbl 0074.​03502 article

H. S. Sha­piro and P. T. Bate­man: “Ad­vanced prob­lems and solu­tions: Solu­tions: 4656,” Amer. Math. Monthly 63 : 10 (1956), pp. 732. MR 1529491 article

J. Lehner and P. T. Bate­man: “Ad­vanced prob­lems and solu­tions: Solu­tions: 4610,” Amer. Math. Monthly 63 : 1 (1956), pp. 49–​50. MR 1529213 article

P. T. Bate­man: “Proof of a con­jec­ture of Gross­wald,” Duke Math. J. 25 : 1 (1958), pp. 67–​72. MR 0091970 Zbl 0080.​03602 article

P. T. Bate­man and E. Gross­wald: “On a the­or­em of Er­dős and Szekeres,” Ill. J. Math. 2 : 1 (1958), pp. 88–​98. MR 0095804 Zbl 0079.​07104 article

E. Land­au: Ele­ment­ary num­ber the­ory. Chelsea (New York), 1958. Eng­lish trans­la­tion; with ad­ded ex­er­cises by P. T. Bate­man and Eu­gene Kohl­beck­er. MR 0092794 Zbl 0079.​06201 book

P. T. Bate­man: “Re­mark on a re­cent note on lin­ear forms,” Am. Math. Mon. 65 : 7 (August–September 1958), pp. 517–​518. MR 0101212 Zbl 0083.​03801 article

M. S. Klamkin, I. S. Gal, S. Ka­plan, H. De­mir, P. T. Bate­man, K. Mahler, and M. P. Drazin: “Ad­vanced prob­lems and solu­tions: Prob­lems for solu­tion: 4816–4821,” Amer. Math. Monthly 65 : 10 (1958), pp. 779–​780. MR 1530157 article

M. S. Klamkin and P. T. Bate­man: “Ad­vanced prob­lems and solu­tions: Solu­tions: 4772,” Amer. Math. Monthly 65 : 10 (1958), pp. 781–​782. MR 1530159 article

P. T. Bate­man: “The­or­ems im­ply­ing the non-van­ish­ing of \( \sum \chi(m)m^{-1} \) for real residue-char­ac­ters,” J. In­di­an Math. Soc. (N.S.) 23 (1959), pp. 101–​115. MR 0124299 Zbl 0228.​10021 article

J. L. Massera, P. T. Bate­man, J. Lamperti, L. Flatto, and D. S. Kahn: “Ad­vanced prob­lems and solu­tions: Prob­lems for solu­tion: 4765, 4840–4844,” Amer. Math. Monthly 66 : 4 (1959), pp. 317–​318. MR 1530303 article

S. W. Go­lomb and P. T. Bate­man: “Ad­vanced prob­lems and solu­tions: Solu­tions: 4801,” Amer. Math. Monthly 66 : 5 (1959), pp. 428–​429. MR 1530341 article

P. Er­dos and P. T. Bate­man: “Ad­vanced prob­lems and solu­tions: Solu­tions: 4785,” Amer. Math. Monthly 66 : 2 (1959), pp. 151–​153. MR 1530231 article

P. T. Bate­man: “Ad­vanced prob­lems and solu­tions: Solu­tions: 4819,” Amer. Math. Monthly 66 : 8 (1959), pp. 733. MR 1530480 article

F. Koehler, O. Taussky, P. T. Bate­man, M. S. Klamkin, L. A. Ru­bel, W. Cheney, and A. Gold­stein: “Ad­vanced prob­lems and solu­tions: Prob­lems for solu­tion: 4845–4850,” Amer. Math. Monthly 66 : 5 (1959), pp. 426–​427. MR 1530338 article

Z. A. Melzak, P. T. Bate­man, D. J. New­man, K. Fan, M. S. Klamkin, and L. A. Ru­bel: “Ad­vanced prob­lems and solu­tions: Prob­lems for solu­tion: 4851–4856,” Amer. Math. Monthly 66 : 6 (1959), pp. 515–​516. MR 1530376 article

P. T. Bate­man and N. J. Fine: “Ad­vanced prob­lems and solu­tions: Solu­tions: 4847,” Amer. Math. Monthly 67 : 3 (1960), pp. 299. MR 1530678 article

P. T. Bate­man, I. Rein­er, and S. Sato: “Ad­vanced prob­lems and solu­tions: Solu­tions: 4852,” Amer. Math. Monthly 67 : 5 (1960), pp. 480–​481. MR 1530771 article

P. T. Bate­man and Y. Chang: “Ad­vanced prob­lems and solu­tions: Solu­tions: 4840,” Amer. Math. Monthly 67 : 2 (1960), pp. 189. MR 1530637 article

B. Gor­don, P. L. Butzer, P. T. Bate­man, J. Rain­wa­ter, D. J. New­man, and J. S. Frame: “Ad­vanced prob­lems and solu­tions: Prob­lems for solu­tion: 4905–4910,” Amer. Math. Monthly 67 : 5 (1960), pp. 479. MR 1530769 article

D. J. New­man, P. T. Bate­man, A. Wil­ansky, P. M. Cohn, R. Spira, and H. A. Po­gorzel­ski: “Ad­vanced prob­lems and solu­tions: Prob­lems for solu­tion: 4971–4976,” Amer. Math. Monthly 68 : 6 (1961), pp. 576–​577. MR 1531275 article

M. S. Klamkin, L. A. Shepp, Y. Mat­suoka, P. T. Bate­man, U. C. Guha, B. L. T. D. Scio, and W. M. Kan­tor: “Ad­vanced prob­lems and solu­tions: Prob­lems for solu­tion: 4983–4988,” Amer. Math. Monthly 68 : 8 (1961), pp. 807–​808. MR 1531373 article

P. T. Bate­man and N. J. Fine: “Ad­vanced prob­lems and solu­tions: Solu­tions: 4907,” Amer. Math. Monthly 68 : 4 (1961), pp. 385–​386. MR 1531208 article

P. T. Bate­man and R. A. Horn: “A heur­ist­ic asymp­tot­ic for­mula con­cern­ing the dis­tri­bu­tion of prime num­bers,” Math. Com­put. 16 : 79 (1962), pp. 363–​367. MR 0148632 Zbl 0105.​03302 article

P. T. Bate­man: “The Minkowski–Hlawka the­or­em in the geo­metry of num­bers,” Arch. Math. 13 (1962), pp. 357–​362. Ded­ic­ated to Re­in­hold Baer on the oc­ca­sion of his six­tieth birth­day. MR 0147457 Zbl 0105.​03604 article

P. T. Bate­man and R. M. Stemmler: “War­ing’s prob­lem for al­geb­ra­ic num­ber fields and primes of the form \( (p^r-1)/(p^d-1) \),” Ill. J. Math. 6 : 1 (1962), pp. 142–​156. Ded­ic­ated to Hans Rademach­er on the oc­ca­sion of his sev­en­ti­eth birth­day. MR 0138616 Zbl 0107.​03903 article

P. T. Bate­man and A. L. Du­quette: “The ana­logue of the Pisot–Vi­jayaraghavan num­bers in fields of form­al power series,” Ill. J. Math. 6 : 4 (1962), pp. 594–​606. MR 0144883 Zbl 0105.​02801 article

P. T. Bate­man and E. Gross­wald: “Ima­gin­ary quad­rat­ic fields with unique fac­tor­iz­a­tion,” Ill. J. Math. 6 : 1 (1962), pp. 187–​192. Ded­ic­ated to Hans Rademach­er on the oc­ca­sion of his sev­en­ti­eth birth­day. MR 0138617 Zbl 0100.​03103 article

S. W. Go­lomb and P. T. Bate­man: “Ad­vanced prob­lems and solu­tions: Solu­tions: 4970,” Amer. Math. Monthly 69 : 8 (1962), pp. 813–​814. MR 1531857 article

P. T. Bate­man and F. W. Owens: “Ad­vanced prob­lems and solu­tions: Solu­tions: 4972,” Amer. Math. Monthly 69 : 8 (1962), pp. 815–​816. MR 1531859 article

P. T. Bate­man, L. Carl­itz, and S. L. Warner: “Ad­vanced prob­lems and solu­tions: Solu­tions: 4985,” Amer. Math. Monthly 69 : 9 (1962), pp. 931–​932. MR 1531910 article

P. T. Bate­man, E. E. Kohl­beck­er, and J. P. Tull: “On a the­or­em of Er­dős and Fuchs in ad­dit­ive num­ber the­ory,” Proc. Am. Math. Soc. 14 : 2 (April 1963), pp. 278–​284. MR 0144876 Zbl 0112.​27405 article

P. T. Bate­man and S. Chow­la: “Some spe­cial tri­go­no­met­ric­al series re­lated to the dis­tri­bu­tion of prime num­bers,” J. Lon­don Math. Soc. 38 : 1 (1963), pp. 372–​374. MR 0153639 Zbl 0116.​26904 article

R. S. Spira, R. G. Al­bert, P. T. Bate­man, M. Gold­berg, R. H. Wilson, Jr., and D. Zeitlin: “Ele­ment­ary prob­lems and solu­tions: Solu­tions: E1517,” Amer. Math. Monthly 70 : 2 (1963), pp. 211–​212. MR 1532024 article

P. M. Cohn and P. T. Bate­man: “Ad­vanced prob­lems and solu­tions: Solu­tions: 5044,” Amer. Math. Monthly 70 : 7 (1963), pp. 773. MR 1532274 article

H. No­land, G. Torch­inelli, and P. T. Bate­man: “Ele­ment­ary prob­lems and solu­tions: Solu­tions: E1567,” Amer. Math. Monthly 70 : 10 (1963), pp. 1103–​1104. MR 1532443 article

H. S. Sha­piro, D. Z. Djokovic, P. T. Bate­man, G. Craw­ford, A. W. Mar­shall, and F. Proschan: “Ad­vanced prob­lems and solu­tions: Solu­tions: 5060,” Amer. Math. Monthly 70 : 9 (1963), pp. 1021–​1022. MR 1532398 article

O. Ore, J. L. Sel­fridge, and P. T. Bate­man: “Ad­vanced prob­lems and solu­tions: Solu­tions: 4995,” Amer. Math. Monthly 70 : 1 (1963), pp. 101–​102. MR 1532000 article

P. T. Bate­man and E. Gross­wald: “On Ep­stein’s zeta func­tion,” Acta Arith. 9 : 4 (1964), pp. 365–​373. Ded­ic­ated to Pro­fess­or L. J. Mor­dell on the oc­ca­sion of his sev­enty-fifth birth­day. MR 0179141 Zbl 0128.​27004 article

P. T. Bate­man: “Se­quences of mass dis­tri­bu­tions on the unit circle which tend to a uni­form dis­tri­bu­tion,” Am. Math. Mon. 71 : 2 (February 1964), pp. 165–​172. MR 0161987 Zbl 0128.​27303 article

P. T. Bate­man, L. A. Ru­bel, K. Koh, J. E. Pot­ter, R. Fitzger­ald, R. Bojan­ic, O. Frink, P. R. Vein, R. Breusch, D. Carlson, and A. E. Liv­ing­ston: “Ad­vanced prob­lems and solu­tions: Prob­lems for solu­tion: 5171–5180,” Amer. Math. Monthly 71 : 2 (1964), pp. 215–​217. MR 1532551 article

P. T. Bate­man and M. E. Low: “Prime num­bers in arith­met­ic pro­gres­sions with dif­fer­ence 24,” Am. Math. Mon. 72 : 2 (February 1965), pp. 139–​143. MR 0173649 Zbl 0127.​26805 article

P. T. Bate­man and R. A. Horn: “Primes rep­res­en­ted by ir­re­du­cible poly­no­mi­als in one vari­able,” pp. 119–​132 in The­ory of num­bers (Pas­adena, CA, 21–22 Novem­ber 1963). Edi­ted by A. L. White­man. Pro­ceed­ings of Sym­po­sia in Pure Math­em­at­ics 8. Amer­ic­an Math­em­at­ic­al So­ci­ety (Provid­ence, RI), 1965. MR 0176966 Zbl 0136.​32902 incollection

P. T. Bate­man and L. A. Ru­bel: “Prob­lems and solu­tions: Solu­tions of ad­vanced prob­lems: 5171,” Amer. Math. Monthly 72 : 2 (1965), pp. 195–​197. MR 1533135 article

P. T. Bate­man: “Lower bounds for \( \sum h(m)/m \) for arith­met­ic­al func­tions \( h \) sim­il­ar to real residue-char­ac­ters,” J. Math. Anal. Ap­pl. 15 : 1 (July 1966), pp. 2–​20. Ded­ic­ated to H. S. Van­diver on his eighty-third birth­day. MR 0199164 Zbl 0144.​27803 article

E. Pitch­er and P. T. Bate­man: “The an­nu­al meet­ing in Hou­s­ton,” Bull. Am. Math. Soc. 73 : 3 (1967), pp. 295–​305. MR 1566431 article

P. T. Bate­man: “The April meet­ing in Chica­go,” Bull. Am. Math. Soc. 73 : 4 (1967), pp. 508. MR 1566437 article

P. T. Bate­man: “The Novem­ber meet­ing in Urb­ana,” Bull. Am. Math. Soc. 74 : 1 (1968), pp. 91. MR 1566459 article

E. Pitch­er and P. Bate­man: “The April meet­ing in Chica­go,” Bull. Am. Math. Soc. 74 : 5 (1968), pp. 880–​883. MR 1566475 article

Z. Ru­bin­stein, L. P. Zukowski, H. Liebeck, J. Barlaz, T. S. Frank, N. S. Mendel­sohn, P. T. Bate­man, G. C. Ber­res­ford, W. E. Buker, L. Carl­itz, and R. A. Scov­ille: “Prob­lems and solu­tions: Ele­ment­ary prob­lems: E2045–E2054,” Amer. Math. Monthly 75 : 1 (1968), pp. 75–​77. MR 1534673 article

P. T. Bate­man: “The Novem­ber meet­ing in Evan­ston,” Bull. Am. Math. Soc. 75 : 2 (1969), pp. 317. MR 1566495 article

P. T. Bate­man and H. G. Dia­mond: “Asymp­tot­ic dis­tri­bu­tion of Beurl­ing’s gen­er­al­ized prime num­bers,” pp. 152–​210 in Stud­ies in num­ber the­ory. Edi­ted by W. J. LeVeque. MAA Stud­ies in Math­em­at­ics 6. Pren­tice-Hall (Engle­wood Cliffs, NJ), 1969. MR 0242778 Zbl 0216.​31403 incollection

P. T. Bate­man: “The April meet­ing in Cin­cin­nati,” Bull. Am. Math. Soc. 75 : 5 (1969), pp. 930–​931. MR 1566523 article

E. Pitch­er and P. Bate­man: “The sum­mer meet­ing in Madis­on,” Bull. Am. Math. Soc. 75 : 1 (1969), pp. 11–​27. MR 1566487 article

P. T. Bate­man: “Prob­lems and solu­tions: Solu­tions of ele­ment­ary prob­lems: E2051,” Amer. Math. Monthly 76 : 2 (1969), pp. 190–​191. MR 1535297 article

P. T. Bate­man: “The April meet­ing in Madis­on,” Bull. Am. Math. Soc. 76 : 5 (1970), pp. 980–​981. MR 1566562 article

P. T. Bate­man: “The Novem­ber meet­ing in Ann Ar­bor,” Bull. Am. Math. Soc. 76 : 3 (1970), pp. 583–​584. MR 1566549 article

P. T. Bate­man, J. W. Brown, R. S. Hall, K. E. Kloss, and R. M. Stemmler: “Lin­ear re­la­tions con­nect­ing the ima­gin­ary parts of the zer­os of the zeta func­tion,” pp. 11–​19 in Com­puters in num­ber the­ory (Ox­ford, 18–23 Au­gust 1969). Edi­ted by A. O. L. Atkin and J. B. Bry­an. Aca­dem­ic Press (Lon­don), 1971. Pro­ceed­ings of the Sci­entif­ic Re­search Coun­cil At­las Sym­posi­um no. 2. MR 0330069 Zbl 0216.​03601 incollection

P. T. Bate­man: “The March meet­ing in Chica­go,” Bull. Am. Math. Soc. 77 : 5 (1971), pp. 695–​696. MR 1566605 article

P. T. Bate­man: “The Novem­ber meet­ing in Urb­ana,” Bull. Am. Math. Soc. 77 : 2 (1971), pp. 182–​183. MR 1566589 article

P. Er­dos and P. T. Bate­man: “Prob­lems and solu­tions: Solu­tions of ad­vanced prob­lems: 5724,” Amer. Math. Monthly 78 : 4 (1971), pp. 412. MR 1536305 article

P. T. Bate­man: “The Novem­ber meet­ing in Mil­wau­kee,” Bull. Am. Math. Soc. 78 : 2 (1972), pp. 184–​185. MR 1566631 article

P. T. Bate­man: “The April meet­ing in St. Louis,” Bull. Am. Math. Soc. 78 : 4 (1972), pp. 508–​510. MR 1566644 article

P. T. Bate­man: “Mul­ti­plic­at­ive arith­met­ic func­tions and the rep­res­ent­a­tion of in­tegers as sums of squares,” pp. 9–​13 in Pro­ceed­ings of the 1972 num­ber the­ory con­fer­ence (Boulder, CO, 14–18 Au­gust 1972). Uni­versity of Col­or­ado, 1972. MR 0389830 Zbl 0323.​10019 incollection

P. T. Bate­man: “The dis­tri­bu­tion of val­ues of the Euler func­tion,” Acta Arith. 21 (1972), pp. 329–​345. Ded­ic­ated to the memory of the late Pro­fess­or Wacław Si­er­piński. MR 0302586 Zbl 0217.​31901 article

P. T. Bate­man: “The April meet­ing in Evan­ston,” Bull. Am. Math. Soc. 79 : 6 (1973), pp. 1172–​1173. MR 1566699 article

P. T. Bate­man: “The Novem­ber meet­ing in Clev­e­land,” Bull. Am. Math. Soc. 79 : 4 (1973), pp. 654. MR 1566682 article

E. Pitch­er and P. T. Bate­man: “The an­nu­al meet­ing in Dal­las,” Bull. Am. Math. Soc. 79 : 4 (1973), pp. 655–​662. MR 1566683 article

P. T. Bate­man: “The Novem­ber meet­ing in Min­neapol­is,” Bull. Am. Math. Soc. 80 : 3 (1974), pp. 444. MR 1566720 article

D. M. Bat­tany and P. T. Bate­man: “Prob­lems and solu­tions: Solu­tions of ad­vanced prob­lems: 5915,” Amer. Math. Monthly 81 : 7 (1974), pp. 788–​789. MR 1537491 article

E. Pitch­er and P. T. Bate­man: “The April meet­ing in St. Louis,” Bull. Am. Math. Soc. 81 : 6 (1975), pp. 1055–​1059. MR 1566826 article

P. T. Bate­man, G. B. Purdy, and S. S. Wag­staff, Jr.: “Some nu­mer­ic­al res­ults on Fekete poly­no­mi­als,” Math. Com­put. Simul. 29 : 129 (January 1975), pp. 7–​23. MR 0480293 Zbl 0301.​10036 article

P. T. Bate­man: “The May meet­ing in DeKalb,” Bull. Am. Math. Soc. 81 : 1 (1975), pp. 71–​72. MR 1566748 article

P. T. Bate­man: “The Novem­ber meet­ing in Hou­s­ton,” Bull. Am. Math. Soc. 81 : 4 (1975), pp. 699. MR 1566790 article

P. T. Bate­man: “The Novem­ber meet­ing in Chica­go,” Bull. Am. Math. Soc. 82 : 3 (1976), pp. 478–​479. MR 1566869 article

E. Pitch­er and P. T. Bate­man: “The Sum­mer meet­ing in Kala­ma­zoo,” Bull. Am. Math. Soc. 82 : 3 (1976), pp. 472–​477. MR 1566867 article

P. T. Bate­man: “The March meet­ing in Urb­ana,” Bull. Am. Math. Soc. 83 : 1 (1977), pp. 113–​114. MR 1566929 article

E. Pitch­er and P. T. Bate­man: “The Janu­ary meet­ing in San Ant­o­nio,” Bull. Am. Math. Soc. 83 : 1 (1977), pp. 107–​112. MR 1566927 article

P. T. Bate­man: “The Er­dős–Fuchs the­or­em on the square of a power series,” J. Num­ber The­ory 9 : 3 (August 1977), pp. 330–​337. MR 0498470 Zbl 0353.​10041 article

P. Bate­man and H. Dia­mond: “John E. Lit­tle­wood (1885–1977): An in­form­al ob­it­u­ary,” Math. In­tell. 1 : 1 (March 1978–1979), pp. 28–​33. MR 0490851 article

I. J. Good and P. T. Bate­man: “Prob­lems and solu­tions: Solu­tions of ad­vanced prob­lems: 6137,” Amer. Math. Monthly 87 : 6 (1980), pp. 495–​496. MR 1539428 article

P. T. Bate­man, P. Er­dős, C. Pom­er­ance, and E. G. Straus: “The arith­met­ic mean of the di­visors of an in­teger,” pp. 197–​220 in Ana­lyt­ic num­ber the­ory (Phil­adelphia, PA, 12–15 May 1980). Edi­ted by M. I. Knopp. Lec­ture Notes in Math­em­at­ics 899. Spring­er (Ber­lin), 1981. Ded­ic­ated to Emil Gross­wald on the oc­ca­sion of his sixty-eighth birth­day. MR 654528 Zbl 0478.​10027 incollection

P. T. Bate­man: “On the size of the coef­fi­cients of the cyc­lo­tom­ic poly­no­mi­al,” pp. 1–​18 in Sem­in­aire de théor­ie des nombres de Bor­deaux (Bor­deaux, 1981–1982), vol. 11: 1981–1982. Uni­versité de Bor­deaux 1 (Talence, France), 1982. Ex­posé no. 28. Note that an art­icle with the same title was pub­lished by Bate­man, Pom­er­ance and Vaughan in 1984. Zbl 0512.​10005 incollection

P. T. Bate­man and C. Pom­er­ance: “Mod­uli \( r \) for which there are many small primes con­gru­ent to \( a \) mod­ulo \( r \),” pp. 8–​19 in Col­loque Hubert Delange (Or­say, France, 7–8 June 1982). Pub­lic­a­tions Math­ématiques d’Or­say 83. So­ciété Math­ématique de France (Par­is), 1983. MR 728397 Zbl 0528.​10028 incollection

P. T. Bate­man and E. Gross­wald: “Pos­it­ive in­tegers ex­press­ible as a sum of three squares in es­sen­tially only one way,” J. Num­ber The­ory 19 : 3 (December 1984), pp. 301–​308. Ded­ic­ated to the memory of Ernst Straus (1922–1983) [mis­prin­ted on pa­per as “Strass”]. MR 769785 Zbl 0558.​10038 article

P. T. Bate­man, C. Pom­er­ance, and R. C. Vaughan: “On the size of the coef­fi­cients of the cyc­lo­tom­ic poly­no­mi­al,” pp. 171–​202 in Top­ics in clas­sic­al num­ber the­ory (Bud­apest, 20–25 Ju­ly 1981), vol. I. Edi­ted by G. Halász. Col­loquia Math­em­at­ica So­ci­e­tatis János Bolyai 34. North-Hol­land (Am­s­ter­dam), 1984. Note that an art­icle with the same title had been pub­lished by Bate­man alone in 1982. MR 781138 Zbl 0547.​10010 incollection

P. T. Bate­man: “Book re­view: Wal­ter K. Bühler, ‘Gauss, a bio­graph­ic­al study’,” Bull. Am. Math. Soc. (N.S.) 14 : 2 (1986), pp. 312–​317. MR 1567583 article

P. T. Bate­man: “Book re­view: Heini Hal­ber­stam, ed., ‘Se­lec­ted Pa­pers of Loo-Keng Hua’,” Am. Math. Mon. 93 : 1 (January 1986), pp. 67–​69. MR 1540794 article

D. Raws­thorne, E. Kron­heimer, P. A. Bat­nik, A. Lu­pas, W. F. Eber­lein, B. Reznick, and J. Todd: “Prob­lems and solu­tions: Ele­ment­ary prob­lems: E3219–E3224,” Amer. Math. Monthly 94 : 7 (1987), pp. 680–​681. P. A. Bat­nik is the pseud­onym of Paul T. Bate­man and Bruce Reznick. MR 1541146 article

D. K. Co­hoon, P. A. Bat­nik, D. E. Knuth, I. Vardi, and N. J. Fine: “Prob­lems and solu­tions: Ad­vanced prob­lems: 6579–6582,” Amer. Math. Monthly 95 : 8 (1988), pp. 773–​774. P. A. Bat­nik is the pseud­onym of Paul T. Bate­man and Bruce Reznick. MR 1541385 article

P. T. Bate­man, J. L. Sel­fridge, and S. S. Wag­staff, Jr.: “The new Mersenne con­jec­ture,” Am. Math. Mon. 96 : 2 (February 1989), pp. 125–​128. This was part of the reg­u­lar AMM fea­ture “The Ed­it­or’s Corner”. MR 992073 Zbl 0694.​10005 article

P. T. Bate­man: “In­tegers ex­press­ible in a giv­en num­ber of ways as a sum of two squares,” pp. 37–​45 in A trib­ute to Emil Gross­wald: Num­ber the­ory and re­lated ana­lys­is. Edi­ted by M. I. Knopp and M. Shein­gorn. Con­tem­por­ary Math­em­at­ics 143. Amer­ic­an Math­em­at­ic­al So­ci­ety (Provid­ence, RI), 1993. Ded­ic­ated to the memory of Eliza­beth and Emil Gross­wald. MR 1210510 Zbl 0790.​11032 incollection

P. T. Bate­man, C. G. Jockusch, and A. R. Woods: “De­cid­ab­il­ity and un­de­cid­ab­il­ity of the­or­ies with a pre­dic­ate for the primes,” J. Symb. Log. 58 : 2 (June 1993), pp. 672–​687. MR 1233932 Zbl 0785.​03002 article

P. T. Bate­man and H. G. Dia­mond: “Book re­view: Joe Roberts, ‘The lure of the in­tegers’,” Am. Math. Mon. 101 : 5 (1994), pp. 480–​482. MR 1542539 article

P. T. Bate­man, A. J. Hildebrand, and G. B. Purdy: “Sums of dis­tinct squares,” Acta Arith. 67 : 4 (1994), pp. 349–​380. MR 1301824 Zbl 0815.​11048 article

P. T. Bate­man: “The asymp­tot­ic for­mula for the num­ber of rep­res­ent­a­tions of an in­teger as a sum of five squares,” pp. 129–​139 in Ana­lyt­ic num­ber the­ory: Pro­ceed­ings of a con­fer­ence in hon­or of Heini Hal­ber­stam (Al­ler­ton Park, IL, 16–20 May 1995), vol. 1. Edi­ted by B. C. Berndt, H. G. Dia­mond, and A. J. Hildebrand. Pro­gress in Math­em­at­ics 138. Birkhäuser (Bo­ston), 1996. Ded­ic­ated to Heini and Doreen Hal­ber­stam. MR 1399334 Zbl 0857.​11019 incollection

P. T. Bate­man and H. G. Dia­mond: “A hun­dred years of prime num­bers,” Am. Math. Mon. 103 : 9 (November 1996), pp. 729–​741. MR 1416621 Zbl 0871.​11005 article

P. T. Bate­man: “A the­or­em of Ing­ham im­ply­ing that Di­rich­let’s \( L \)-func­tions have no zer­os with real part one,” En­sei­gn. Math. (2) 43 : 3–​4 (1997), pp. 281–​284. MR 1489887 Zbl 0908.​11041 article

N. Abe and P. T. Bate­man: “Prob­lems and solu­tions: Solu­tions: 10376,” Amer. Math. Monthly 104 : 3 (1997), pp. 276–​277. MR 1542982 article

R. Pinkham, D. E. Knuth, D. Witte, H. S. Wilf, P. Bate­man, D. Cox, J. C. Lagari­as, and T. J. Richard­son: “Prob­lems and solu­tions: Prob­lems: 10585–10591,” Amer. Math. Monthly 104 : 5 (1997), pp. 456–​457. MR 1543017 article

P. T. Bate­man and M. I. Knopp: “Some new old-fash­ioned mod­u­lar iden­tit­ies,” Ramanu­jan J. 2 : 1–​2 (1998), pp. 247–​269. Ded­ic­ated to the memory of Paul Er­dős. MR 1642881 Zbl 0909.​11018 article

P. Bate­man, D. Brad­ley, D. Cal­lan, and R. Stong: “Prob­lems and solu­tions: Solu­tions: Bin­ary ex­pan­sions and \( k \)-th powers: 10596,” Amer. Math. Monthly 106 : 4 (1999), pp. 366–​367. MR 1543465 article

P. T. Bate­man and H. G. Dia­mond: “On the os­cil­la­tion the­or­ems of Pring­sheim and Land­au,” pp. 43–​54 in Num­ber the­ory. Edi­ted by R. P. Bam­bah, V. C. Du­mir, and R. J. Hans-Gill. Trends in Math­em­at­ics. Birkhäuser (Basel), 2000. MR 1764795 Zbl 0964.​11037 incollection

P. Bate­man and J. Kalb: “Prob­lems and solu­tions: Prob­lems: 10797,” Amer. Math. Monthly 107 : 4 (2000), pp. 367. MR 1543650 article

P. Bate­man and D. Eich­horn: “Prob­lems and solu­tions: Prob­lems: 10778,” Amer. Math. Monthly 107 : 1 (2000), pp. 83. MR 1543595 article

P. T. Bate­man, B. A. Dat­skovsky, and M. I. Knopp: “Sums of squares and the pre­ser­va­tion of mod­u­lar­ity un­der con­gru­ence re­stric­tions,” pp. 59–​71 in Sym­bol­ic com­pu­ta­tion, num­ber the­ory, spe­cial func­tions, phys­ics and com­bin­at­or­ics (Gaines­ville, FL, 11–13 Novem­ber 1999). Edi­ted by F. G. Gar­van and M. E. H. Is­mail. De­vel­op­ments in Math­em­at­ics 4. Kluwer Aca­dem­ic (Dordrecht), 2001. MR 1880079 Zbl 1040.​11018 incollection

P. T. Bate­man: “Some per­son­al memor­ies of Paul Er­dős,” pp. 9–​12 in Paul Er­dős and his math­em­at­ics (Bud­apest, 4–11 Ju­ly 1999), vol. I. Edi­ted by G. Halász, L. Lovász, M. Si­monovits, and V. T. Sós. Bolyai So­ci­ety Math­em­at­ic­al Stud­ies 11. Spring­er (Ber­lin), 2002. MR 1954676 Zbl 1031.​01503 incollection

P. T. Bate­man and H. G. Dia­mond: Ana­lyt­ic num­ber the­ory: An in­tro­duct­ory course. Mono­graphs in Num­ber The­ory 1. World Sci­entif­ic (River Edge, NJ), 2004. MR 2111739 Zbl 1074.​11001 book

J. Schwartz, M. Ger­sten­hab­er, P. Bate­man, J. T. Tate, A. Ma­gid, G. D. Mostow, W. Fer­rer San­tos, C. Moore, B. Kostant, G. M. Berg­man, M. Moskow­itz, and N. Nahlus: “Ger­hard Hoch­schild (1915–2010),” No­tices Am. Math. Soc. 58 : 8 (2011), pp. 1078–​1099. Fer­rer San­tos and Moskow­itz were co­ordin­at­ing ed­it­ors. MR 2856143 Zbl 1225.​01083 article

Paul Bate­man,” The News-Gaz­ette (27 December 2012). article

Paul Bate­man,” The News-Gaz­ette (20 January 2013). article