The Lerch zeta function I. Zeta integrals

DOI10.1515/form.2011.047zbMath1253.11085arXiv1005.4712OpenAlexW2950994537MaRDI QIDQ2882745

Jeffrey C. Lagarias, Wen-Ch'ing Winnie Li

Publication date: 7 May 2012

Published in: Forum Mathematicum (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1005.4712

zbMATH Keywords

Hurwitz zeta functionperiodic zeta functionfunctional equationLerch zeta function

Mathematics Subject Classification ID

Hurwitz and Lerch zeta functions (11M35)

Related Items (12)

The Lerch zeta function. III: Polylogarithms and special values ⋮ Bose-Einstein condensation for an exponential density of states function and Lerch zeta function ⋮ The Lerch zeta function. IV: Hecke operators ⋮ Evaluation of integrals with hypergeometric and logarithmic functions ⋮ On the density arising from the domain of attraction of an operator interpolating between sum and supremum: the \(\alpha\)-sun operator ⋮ The joint universality of Dirichlet \(L\)-functions and Lerch zeta-functions ⋮ Crandall's computation of the incomplete gamma function and the Hurwitz zeta function, with applications to Dirichlet \(L\)-series ⋮ Symmetry of zeros of Lerch zeta-function for equal parameters ⋮ Summation and the Poisson formula ⋮ The Lerch zeta function as a fractional derivative ⋮ Riemann-Siegel integral formula for the Lerch zeta function ⋮ Asymptotic relations between interpolation differences and zeta functions

Cites Work

• On Riemann's zeta function
• On the \(\Gamma\)-factors attached to motives
• Local \(L\)-factors of motives and regularized determinants
• A local Riemann hypothesis. I
• Growth of the Lerch zeta-function
• Expansion of the Riemann Ξ Function in Meixner–Pollaczek Polynomials
• LOCAL RIEMANN HYPOTHESIS FOR COMPLEX NUMBERS
• On Fourier and Zeta(s)
• Integral representations for the Dirichlet L-functions and their expansions in Meixner–Pollaczek polynomials and rising factorials†

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