Generalized Lerch formulas: examples of zeta-regularized products

DOI10.1016/J.JNT.2005.08.005zbMath1143.11033OpenAlexW2094326034MaRDI QIDQ852525

Yoshinori Mizuno

Publication date: 15 November 2006

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

Full work available at URL: https://doi.org/10.1016/j.jnt.2005.08.005

zbMATH Keywords

Lerch formulazeta-regularized product

Mathematics Subject Classification ID

Gamma, beta and polygamma functions (33B15) Basic hypergeometric functions in one variable, ({}_rphi_s) (33D15) Selberg zeta functions and regularized determinants; applications to spectral theory, Dirichlet series, Eisenstein series, etc. (explicit formulas) (11M36) Hurwitz and Lerch zeta functions (11M35) Elliptic functions and integrals (33E05)

Related Items (3)

A \(q\)-Raabe formula and an integral of the fourth Jacobi theta function ⋮ Multiplicative anomaly matches Casimir energy for GJMS operators on spheres ⋮ Approximating the constants of Glaisher-Kinkelin type

Cites Work

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• The \(q\)-gamma function for \(q>1\)
• A proof of the classical Kronecker limit formula
• Zeta regularized products and functional determinants on spheres
• Generalized zeta regularizations, quantum class number formulas, and Appell's \(O\)-functions
• A Generalization of Lerch?s Formula

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