Character analogues of theorems of Ramanujan, Koshliakov and Guinand

DOI10.1016/j.aam.2009.12.003zbMath1216.33012OpenAlexW2019254677MaRDI QIDQ534177

Atul Dixit, Jaebum Sohn, Bruce C. Berndt

Publication date: 17 May 2011

Published in: Advances in Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.aam.2009.12.003

zbMATH Keywords

modified Bessel functionsRamanujan's lost notebookdivisor functionsGuinand's formulaKoshliakov's formula

Mathematics Subject Classification ID

(zeta (s)) and (L(s, chi)) (11M06) Bessel and Airy functions, cylinder functions, ({}_0F_1) (33C10)

Related Items (7)

Error functions, Mordell integrals and an integral analogue of a partial theta function ⋮ Riesz-type criteria and theta transformation analogues ⋮ Certain extensions of results of Siegel, Wilton and Hardy ⋮ Identities associated to a generalized divisor function and modified Bessel function ⋮ Unnamed Item ⋮ A Voronoi-type summation formula involving σ_iτ(n) and index transforms ⋮ A class of identities associated with Dirichlet series satisfying Hecke’s functional equation

Cites Work

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• Character analogues of the Poisson and Euler-MacLaurin summation formulas with applications
• Periodic analogues of the Euler-Maclaurin and Poisson summation formulas with applications to number theory
• Koshliakovs Formula and Guinands Formula in Ramanujans Lost Notebook
• SOME SELF-RECIPROCAL FUNCTIONS
• On Some Generalizations of the Cauchy-Frullani Integral
• SOME RAPIDLY CONVERGENT SERIES FOR THE RIEMANN ξ-FUNCTION

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