On squares of odd zeta values and analogues of Eisenstein series

DOI10.1016/j.aam.2019.06.003zbMath1470.11219OpenAlexW2953783022MaRDI QIDQ2326905

Rajat Gupta, Atul Dixit

Publication date: 10 October 2019

Published in: Advances in Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.aam.2019.06.003

zbMATH Keywords

irrationalitymodified Bessel functionDedekind eta functionRamanujan's formulaodd zeta values

Mathematics Subject Classification ID

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

Related Items (4)

Hurwitz zeta functions and Ramanujan's identity for odd zeta values ⋮ Identities associated to a generalized divisor function and modified Bessel function ⋮ On Ramanujan's formula for \(\zeta(1/2)\) and \(\zeta(2m+1)\) ⋮ Dirichlet series under standard convolutions: variations on Ramanujan's identity for odd zeta values

Cites Work

• New pathways and connections in number theory and analysis motivated by two incorrect claims of Ramanujan
• Self-reciprocal functions, powers of the Riemann zeta function and modular-type transformations
• Some mathematical constants
• Modular transformations and generalizations of several formulae of Ramanujan
• Formulas for non-holomorphic Eisenstein series and for the Riemann zeta function at odd integers
• On some relations which are equivalent to functional equations involving the Riemann zeta function
• Euler’s constant: Euler’s work and modern developments
• Transcendental values of certain Eichler integrals
• On some applications of formulae of Ramanujan in the analysis of algorithms
• Ramanujan’s Formula for ζ(2n + 1)
• Comments on some formulae of Ramanujan
• Some Solutions of the Equation F (t ) = F (t ⁻¹ )
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