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

页码：79 / 102

页数：23

共 50 条

[31] Weighted transplantation for Fourier-Bessel series
Óscar Ciaurri
Krzysztof Stempak
[J]. Journal d’Analyse Mathématique, 2006, 100 : 133 - 156
[32] Sums of the kth divisor function of the ternary quadratic with prime variables
Yuetong Zhao
Wenguang Zhai
Jinjiang Li
[J]. The Ramanujan Journal, 2023, 60 : 485 - 504
[33] Sums of the kth divisor function of the ternary quadratic with prime variables
Zhao, Yuetong
Zhai, Wenguang
Li, Jinjiang
[J]. RAMANUJAN JOURNAL, 2023, 60 (02): : 485 - 504
[34] THE RELATION PROPERTY BETWEEN THE DIVISOR FUNCTION AND INFINITE PRODUCT SUMS
Kim, Aeran
[J]. HONAM MATHEMATICAL JOURNAL, 2016, 38 (03): : 507 - 552
[35] The circle method and shifted convolution sums involving the divisor function
Hu, Guangwei
Lao, Huixue
[J]. JOURNAL OF NUMBER THEORY, 2024, 262 : 1 - 27
[36] Restricted divisor sums
Broughan, KA
[J]. ACTA ARITHMETICA, 2002, 101 (02) : 105 - 114
[37] SUCCESSIVE DIVISOR SUMS
不详
[J]. AMERICAN MATHEMATICAL MONTHLY, 1991, 98 (03): : 273 - 276
[38] Exponential sums involving the divisor function over arithmetic progressions
Zhang, Rui
Li, Yang
Yan, Xiaofei
[J]. AIMS MATHEMATICS, 2023, 8 (05): : 11084 - 11094
[39] RECURRENT FORMULAS FOR POWER SUMS OF BESSEL FUNCTION ROOTS
MEIMAN, NN
[J]. DOKLADY AKADEMII NAUK SSSR, 1956, 108 (02): : 190 - 193
[40] SUMS OF CERTAIN SERIES OF BESSEL FUNCTIONS ENCOUNTERED IN DIFFRACTION THEORY
BENENSON, LS
[J]. RADIO ENGINEERING AND ELECTRONIC PHYSICS-USSR, 1969, 14 (07): : 1140 - &

← 1 2 3 4 5 →