Special values of trigonometric Dirichlet series and Eichler integrals

DOI10.1007/s11139-015-9698-4zbMath1418.11067arXiv1407.5119OpenAlexW2095913594MaRDI QIDQ2520575

Armin Straub

Publication date: 16 December 2016

Published in: The Ramanujan Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1407.5119

zbMATH Keywords

Eichler integralstrigonometric Dirichlet series

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)

Related Items (5)

Explicit transformations of certain Lambert series ⋮ Unnamed Item ⋮ The approximate functional equation of some Diophantine series ⋮ A new Ramanujan-type identity for \(L(2k+1, \chi_1)\) ⋮ The convergence of certain Diophantine series

Cites Work

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• On a secant Dirichlet series and Eichler integrals of Eisenstein series
• Rationality of secant zeta values
• Modular transformations and generalizations of several formulae of Ramanujan
• Secant zeta functions
• Modular forms and period polynomials
• On the convergence of Diophantine Dirichlet series
• Elliptic Modular Forms and Their Applications
• Transcendental values of certain Eichler integrals
• Dedekind Sums and a Paper of G. H. Hardy
• Analytic Eisenstein series, theta-functions, and series relations in the spirit of Ramanujan.
• Barnes multiple zeta-functions, Ramanujan's formula, and relevant series involving hyperbolic functions

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