Celebratio Mathematica

Paul T. Bateman

Number theory  ·  UIUC

Sums of squares and modular number theory

[1]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

[2]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

[3]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

[4]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

[5]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

[6]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

[7]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

[8]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

[9]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