Weighted divisor sums and Bessel function series, IV

Bruce C. Berndt; Sun Kim; Alexandru Zaharescu

doi:10.1007/s11139-011-9352-8

Weighted divisor sums and Bessel function series, IV

Bruce C. Berndt
, Sun Kim^*
, Alexandru Zaharescu

^*Corresponding author for this work

Department of Mathematics

University of Illinois at Urbana-Champaign
Ohio State University
Romanian Academy

Research output: Contribution to journal › Journal article › peer-review

12 Scopus citations

Abstract

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.

Original language	English
Pages (from-to)	79-102
Number of pages	24
Journal	Ramanujan Journal
Volume	29
Issue number	1-3
DOIs	https://doi.org/10.1007/s11139-011-9352-8
State	Published - 2012.12

Keywords

Bessel functions
Circle problem
Dirichlet L-series
Ramanujan's Lost Notebook
Riesz sums
Weighted divisor sums

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10.1007/s11139-011-9352-8

Cite this

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title = "Weighted divisor sums and Bessel function series, IV",

abstract = "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.",

keywords = "Bessel functions, Circle problem, Dirichlet L-series, Ramanujan's Lost Notebook, Riesz sums, Weighted divisor sums",

author = "Berndt, \{Bruce C.\} and Sun Kim and Alexandru Zaharescu",

year = "2012",

month = dec,

doi = "10.1007/s11139-011-9352-8",

language = "English",

volume = "29",

pages = "79--102",

journal = "Ramanujan Journal",

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T1 - Weighted divisor sums and Bessel function series, IV

AU - Berndt, Bruce C.

AU - Kim, Sun

AU - Zaharescu, Alexandru

PY - 2012/12

Y1 - 2012/12

N2 - 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.

AB - 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.

KW - Bessel functions

KW - Circle problem

KW - Dirichlet L-series

KW - Ramanujan's Lost Notebook

KW - Riesz sums

KW - Weighted divisor sums

UR - https://www.scopus.com/pages/publications/84869118190

U2 - 10.1007/s11139-011-9352-8

DO - 10.1007/s11139-011-9352-8

M3 - Journal article

AN - SCOPUS:84869118190

SN - 1382-4090

VL - 29

SP - 79

EP - 102

JO - Ramanujan Journal

JF - Ramanujan Journal

IS - 1-3

ER -

Weighted divisor sums and Bessel function series, IV

Abstract

Keywords

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