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

Mathematics

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

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 (US)
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
State	Published - Jan 2011

Keywords

Character analogues
Divisor functions
Guinands formula
Koshliakovs formula
Modified Bessel functions
Ramanujans Lost Notebook

ASJC Scopus subject areas

Applied Mathematics

Online availability

10.1016/j.aam.2009.12.003

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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.",

keywords = "Character analogues, Divisor functions, Guinands formula, Koshliakovs formula, Modified Bessel functions, Ramanujans Lost Notebook",

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

note = "E-mail addresses: [email protected] (B.C. Berndt), [email protected] (A. Dixit), [email protected] (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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journal = "Advances in Applied Mathematics",

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AU - Berndt, Bruce C.

AU - Dixit, Atul

AU - Sohn, Jaebum

N1 - E-mail addresses: [email protected] (B.C. Berndt), [email protected] (A. Dixit), [email protected] (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.

PY - 2011/1

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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.

KW - Character analogues

KW - Divisor functions

KW - Guinands formula

KW - Koshliakovs formula

KW - Modified Bessel functions

KW - Ramanujans Lost Notebook

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DO - 10.1016/j.aam.2009.12.003

M3 - Article

AN - SCOPUS:79953684865

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JO - Advances in Applied Mathematics

JF - Advances in Applied Mathematics

IS - 1-4

ER -

Character analogues of theorems of Ramanujan, Koshliakov and Guinand

Abstract

Keywords

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