On series identities arising from Jacobi’s identity of the theta function

DOI10.1142/S1793042118500823zbMath1454.11168OpenAlexW2774383695MaRDI QIDQ4643783

Hirofumi Tsumura

Publication date: 29 May 2018

Published in: International Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s1793042118500823

zbMATH Keywords

Riemann zeta functionBernoulli numbersEuler numbersJacobi theta functionRamanujan Polynomials

Mathematics Subject Classification ID

Bernoulli and Euler numbers and polynomials (11B68) (zeta (s)) and (L(s, chi)) (11M06) Other Dirichlet series and zeta functions (11M41)

Cites Work

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• On alternating analogues of Tornheim's double series. II
• Modular transformations and generalizations of several formulae of Ramanujan
• Zeros of Bernoulli, generalized Bernoulli and Euler polynomials
• Generalized Eisenstein series and modified Dedekind sums.
• Analytic Eisenstein series, theta-functions, and series relations in the spirit of Ramanujan.
• On functional relations between the Mordell–Tornheim double zeta functions and the Riemann zeta function
• Generalized Dedekind Eta-Functions and Generalized Dedekind Sums
• THREE SUMMATIONS DUE TO RAMANUJAN

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