Generalized Lambert series and arithmetic nature of odd zeta values

DOI10.1017/prm.2018.146zbMath1437.11124arXiv1709.00022OpenAlexW2795463244MaRDI QIDQ5221041

Atul Dixit, Bibekananda Maji

Publication date: 27 March 2020

Published in: Proceedings of the Royal Society of Edinburgh: Section A Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1709.00022

zbMATH Keywords

Lambert seriestranscendenceDedekind eta functionEuler's constantRamanujan's formulaodd zeta values

Mathematics Subject Classification ID

(zeta (s)) and (L(s, chi)) (11M06) Transcendence (general theory) (11J81)

Related Items (8)

Explicit transformations for generalized Lambert series associated with the divisor function \(\sigma_a^{(N)}(n)\) and their applications ⋮ Extended higher Herglotz functions. I: Functional equations ⋮ A new Ramanujan-type identity for \(L(2k+1, \chi_1)\) ⋮ GENERALIZED LAMBERT SERIES, RAABE’S COSINE TRANSFORM AND A GENERALIZATION OF RAMANUJAN’S FORMULA FOR ⋮ Identities associated to a generalized divisor function and modified Bessel function ⋮ On Ramanujan's formula for \(\zeta(1/2)\) and \(\zeta(2m+1)\) ⋮ Koshliakov zeta functions I: modular relations ⋮ Dirichlet series under standard convolutions: variations on Ramanujan's identity for odd zeta values

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