Celebratio Mathematica

Paul T. Bateman

Number theory  ·  UIUC

Arithmetic functions and summatory functions

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

[4]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

[5]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

[6]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

[7]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