Koshliakovs Formula and Guinands Formula in Ramanujans Lost Notebook
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Publication:3401682
DOI10.1007/978-0-387-78510-3_2zbMath1183.33007OpenAlexW126860937MaRDI QIDQ3401682
Bruce C. Berndt, Jaebum Sohn, Yoonbok Lee
Publication date: 1 February 2010
Published in: Surveys in Number Theory (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/978-0-387-78510-3_2
modified Bessel functionsMaass wave formsdivisor functionsGuinand's formulaKoshliakov's formulanonanalytic Eisenstein series
Dedekind eta function, Dedekind sums (11F20) Bessel and Airy functions, cylinder functions, ({}_0F_1) (33C10) Automorphic forms, one variable (11F12)
Related Items (17)
Explicit transformations of certain Lambert series ⋮ A generalized modified Bessel function and a higher level analogue of the theta transformation formula ⋮ Two general series identities involving modified Bessel functions and a class of arithmetical functions ⋮ On the Epstein zeta function and the zeros of a class of Dirichlet series ⋮ Koshliakov kernel and identities involving the Riemann zeta function ⋮ Arithmetic and analysis of the series \(\sum_{n=1}^{\infty} \frac{1}{n} \sin \frac{x}{n} \). II ⋮ Character analogues of Cohen-type identities and related Voronoï summation formulas ⋮ Certain extensions of results of Siegel, Wilton and Hardy ⋮ Identities associated to a generalized divisor function and modified Bessel function ⋮ Transformation formulas associated with integrals involving the Riemann \(\Xi\)-function ⋮ Self-reciprocal functions, powers of the Riemann zeta function and modular-type transformations ⋮ Character analogues of theorems of Ramanujan, Koshliakov and Guinand ⋮ Series transformations and integrals involving the Riemann \(\Xi \)-function ⋮ Sums of squares and products of Bessel functions ⋮ The generalized modified Bessel function and its connection with Voigt line profile and Humbert functions ⋮ A general class of Voronoi's and Koshliakov–Ramanujan's summation formulas involvingdk(n) ⋮ Extensions of Watson’s theorem and the Ramanujan–Guinand formula
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