Explicit transformations of certain Lambert series

DOI10.1007/s40687-022-00331-5zbMath1492.33006arXiv2012.12064OpenAlexW4280619618MaRDI QIDQ2146913

Rahul Kumar, Atul Dixit, Aashita Kesarwani

Publication date: 22 June 2022

Published in: Research in the Mathematical Sciences (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2012.12064

zbMATH Keywords

modular transformationsBessel functionsWatson kernelRamanujan's formula for odd zeta valuessums-of-squares function

Mathematics Subject Classification ID

(zeta (s)) and (L(s, chi)) (11M06) Integral transforms of special functions (44A20) Holomorphic modular forms of integral weight (11F11) Generalized hypergeometric series, ({}_pF_q) (33C20) Bessel and Airy functions, cylinder functions, ({}_0F_1) (33C10)

Related Items

Explicit transformations for generalized Lambert series associated with the divisor function \(\sigma_a^{(N)}(n)\) and their applications ⋮ Hurwitz zeta functions and Ramanujan's identity for odd zeta values ⋮ Extended higher Herglotz functions. I: Functional equations ⋮ Extensions of Watson’s theorem and the Ramanujan–Guinand formula

Uses Software

• DLMF

Cites Work

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