Character analogues of theorems of Ramanujan, Koshliakov and Guinand

Bruce C. Berndt; Atul Dixit; Jaebum Sohn

doi:10.1016/j.aam.2009.12.003

Character analogues of theorems of Ramanujan, Koshliakov and Guinand

Bruce C. Berndt, Atul Dixit, Jaebum Sohn

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

7 Citations (Scopus)

Abstract

We derive analogues of theorems of Ramanujan, Koshliakov, and Guinand involving primitive characters and modified Bessel functions. As particular examples, transformation formulas involving the Legendre symbol and sums-of-divisors functions are established.

Original language	English
Pages (from-to)	54-70
Number of pages	17
Journal	Advances in Applied Mathematics
Volume	46
Issue number	1-4
DOIs	https://doi.org/10.1016/j.aam.2009.12.003
Publication status	Published - 2011 Jan

Bibliographical note

Funding Information:
E-mail addresses: berndt@illinois.edu (B.C. Berndt), aadixit2@illinois.edu (A. Dixit), jsohn@yonsei.ac.kr (J. Sohn). 1 Research partially supported by grant H98230-07-1-0088 from the National Security Agency. 2 Research supported by Korea Research Foundation Grant KRF-2006-312-C00006.

All Science Journal Classification (ASJC) codes

Applied Mathematics

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10.1016/j.aam.2009.12.003

Cite this

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title = "Character analogues of theorems of Ramanujan, Koshliakov and Guinand",

abstract = "We derive analogues of theorems of Ramanujan, Koshliakov, and Guinand involving primitive characters and modified Bessel functions. As particular examples, transformation formulas involving the Legendre symbol and sums-of-divisors functions are established.",

author = "Berndt, {Bruce C.} and Atul Dixit and Jaebum Sohn",

note = "Funding Information: E-mail addresses: berndt@illinois.edu (B.C. Berndt), aadixit2@illinois.edu (A. Dixit), jsohn@yonsei.ac.kr (J. Sohn). 1 Research partially supported by grant H98230-07-1-0088 from the National Security Agency. 2 Research supported by Korea Research Foundation Grant KRF-2006-312-C00006.",

year = "2011",

month = jan,

doi = "10.1016/j.aam.2009.12.003",

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AU - Berndt, Bruce C.

AU - Dixit, Atul

AU - Sohn, Jaebum

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N2 - We derive analogues of theorems of Ramanujan, Koshliakov, and Guinand involving primitive characters and modified Bessel functions. As particular examples, transformation formulas involving the Legendre symbol and sums-of-divisors functions are established.

AB - We derive analogues of theorems of Ramanujan, Koshliakov, and Guinand involving primitive characters and modified Bessel functions. As particular examples, transformation formulas involving the Legendre symbol and sums-of-divisors functions are established.

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Character analogues of theorems of Ramanujan, Koshliakov and Guinand

Abstract

Bibliographical note

All Science Journal Classification (ASJC) codes

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