Celebratio Mathematica

Paul T. Bateman

Primes and multiplicative number theory

[1]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

[2]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

[3]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

[4]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

[5]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

[6]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

[7]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

[8]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

[9]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

[10]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

[11]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

[12]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

[13]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

[14]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

[15]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