Ramanujan’s Formula for ζ(2n + 1)
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Publication:5038222
DOI10.1007/978-3-319-59969-4_2zbMath1497.11198arXiv1701.02964OpenAlexW2755681032MaRDI QIDQ5038222
Publication date: 30 September 2022
Published in: Exploring the Riemann Zeta Function (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1701.02964
(zeta (s)) and (L(s, chi)) (11M06) Convergence and divergence of series and sequences (40A05) Evaluation of number-theoretic constants (11Y60)
Related Items (19)
Eichler cohomology and zeros of polynomials associated to derivatives of \(L\)-functions ⋮ Explicit transformations of certain Lambert series ⋮ Series representations and asymptotically finite representations for the numbers \(\zeta (2m + 1)\) and \(\beta (2m)\) ⋮ An elementary proof of Ramanujan's identity for odd zeta values ⋮ Ramanujan's formula for odd zeta values: a proof by Mittag-Leffler expansion and applications ⋮ 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 ⋮ 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 ⋮ Generalized Lambert series and arithmetic nature of odd zeta values ⋮ Formulas for non-holomorphic Eisenstein series and for the Riemann zeta function at odd integers ⋮ On the zeros of period functions associated to the Eisenstein series for \(\Gamma_0^+(N)\) ⋮ Period polynomials, derivatives of \(L\)-functions, and zeros of polynomials ⋮ Living with Ramanujan for 40 years ⋮ On squares of odd zeta values and analogues of Eisenstein series ⋮ Dirichlet series under standard convolutions: variations on Ramanujan's identity for odd zeta values
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