Weighted divisor sums and Bessel function series, IV

被引：0
|
作者：
Bruce C. Berndt
Sun Kim
Alexandru Zaharescu
机构：
[1] University of Illinois,Department of Mathematics
[2] Ohio State University,Department of Mathematics
[3] Institute of Mathematics of the Romanian Academy,undefined
来源：
The Ramanujan Journal | 2012年 / 29卷
关键词：
Circle problem; Bessel functions; Riesz sums; Weighted divisor sums; Dirichlet ; -series; Ramanujan’s Lost Notebook; 11P21; 11M06;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
One fragment (p. 335) published with Ramanujan’s Lost Notebook contains two formulas, each involving a finite trigonometric sum and a doubly infinite series of Bessel functions. The identities are connected with the classical circle and divisor problems, respectively. This paper is devoted to the first identity. First, we obtain a generalization in the setting of Riesz sums. Second, we prove a trigonometric analogue.
引用
收藏
页码：79 / 102
页数：23
相关论文
共 50 条
  • [1] Weighted divisor sums and Bessel function series, IV
    Berndt, Bruce C.
    Kim, Sun
    Zaharescu, Alexandru
    [J]. RAMANUJAN JOURNAL, 2012, 29 (1-3): : 79 - 102
  • [2] Weighted Divisor Sums and Bessel Function Series
    Bruce C. Berndt
    Alexandru Zaharescu
    [J]. Mathematische Annalen, 2006, 335 : 249 - 283
  • [3] Weighted divisor sums and Bessel function series
    Berndt, BC
    Zaharescu, A
    [J]. MATHEMATISCHE ANNALEN, 2006, 335 (02) : 249 - 283
  • [4] Weighted divisor sums and Bessel function series, V
    Berndt, Bruce C.
    Kim, Sun
    Zaharescu, Alexandru
    [J]. JOURNAL OF APPROXIMATION THEORY, 2015, 197 : 101 - 114
  • [5] Weighted divisor sums and Bessel function series, II
    Berndt, Bruce C.
    Kim, Sun
    Zaharescu, Alexandru
    [J]. ADVANCES IN MATHEMATICS, 2012, 229 (03) : 2055 - 2097
  • [6] Weighted divisor sums and Bessel function series. III
    Berndt, Bruce C.
    Kim, Sun
    Zaharescu, Alexandru
    [J]. JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK, 2013, 683 : 67 - 96
  • [7] Divisor weighted sums
    Friedlander J.B.
    Iwaniec H.
    [J]. Journal of Mathematical Sciences, 2006, 137 (2) : 4739 - 4743
  • [8] Sums of divisors functions and Bessel function series
    Kim, Sun
    [J]. JOURNAL OF NUMBER THEORY, 2017, 170 : 142 - 184
  • [9] SUMS OF DIVISOR FUNCTION
    GORDON, B
    ROGERS, K
    [J]. CANADIAN JOURNAL OF MATHEMATICS, 1964, 16 (01): : 151 - &
  • [10] A remark on divisor-weighted sums
    Pollack, Paul
    [J]. RAMANUJAN JOURNAL, 2016, 40 (01): : 63 - 69
12345