On a secant Dirichlet series and Eichler integrals of Eisenstein series

DOI10.1007/s00209-016-1675-0zbMath1402.11060arXiv1406.2273OpenAlexW1491673775MaRDI QIDQ343611

Armin Straub, Bruce C. Berndt

Publication date: 28 November 2016

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1406.2273

zbMATH Keywords

Eisenstein seriesRamanujan polynomialsEichler integralstrigonometric Dirichlet seriesunimodular polynomials

Mathematics Subject Classification ID

Other functions defined by series and integrals (33E20) Holomorphic modular forms of integral weight (11F11) Trigonometric and exponential sums (general theory) (11L03) Higher logarithm functions (33B30)

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Ramanujan’s Formula for ζ(2n + 1) ⋮ Infinite series representations for Dirichlet \(L\)-functions at rational arguments ⋮ Unnamed Item ⋮ An elementary proof of Ramanujan's identity for odd zeta values ⋮ 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 ⋮ Rational functions and modular forms ⋮ Identities associated to a generalized divisor function and modified Bessel function ⋮ On Ramanujan's formula for \(\zeta(1/2)\) and \(\zeta(2m+1)\) ⋮ Zeros and irreducibility of polynomials with gcd powers as coefficients ⋮ Special values of trigonometric Dirichlet series and Eichler integrals ⋮ Rationality of secant zeta values ⋮ Generalized Lambert series and arithmetic nature of odd zeta values ⋮ Ramanujan identities of higher degree ⋮ Dirichlet series under standard convolutions: variations on Ramanujan's identity for odd zeta values

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