Complete asymptotic expansions associated with Epstein zeta-functions

DOI10.1007/s11139-007-9027-7zbMath1171.11023OpenAlexW2116795744MaRDI QIDQ926488

Masanori Katsurada

Publication date: 20 May 2008

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

Full work available at URL: https://doi.org/10.1007/s11139-007-9027-7

zbMATH Keywords

asymptotic expansionRiemann zeta-functionMellin-Barnes integralEpstein zeta-functionLaplace-Mellin transformweighted mean value

Mathematics Subject Classification ID

Analytic theory (Epstein zeta functions; relations with automorphic forms and functions) (11E45) Holomorphic modular forms of integral weight (11F11)

Related Items

Complete asymptotic expansions associated with various zeta-functions ⋮ Transformation formulae and asymptotic expansions for double holomorphic Eisenstein series of two complex variables ⋮ Asymptotic expansions for a class of zeta-functions ⋮ Complete asymptotic expansions associated with Epstein zeta-functions. II ⋮ A study on twisted Koecher-Maass series of Siegel cusp forms via an integral kernel ⋮ Optimal and non-optimal lattices for non-completely monotone interaction potentials ⋮ DIFFERENTIAL ACTIONS ON THE ASYMPTOTIC EXPANSIONS OF NON-HOLOMORPHIC EISENSTEIN SERIES

Cites Work

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• Spectral mean values of Maass waveform \(L\)-functions
• An application of the Mellin-Barnes type of integral to the mean square of \(L\)-functions
• Power series and asymptotic series associated with the Lerch zeta-function
• An explicit formula for the fourth power mean of the Riemann zeta- function
• An application of Mellin-Barnes' type integrals to the mean square of Lerch zeta-functions
• Power series with the Riemann zeta-function in the coefficients
• On the Lerch zeta function
• On an asymptotic formula of Ramanujan for a certain theta-type series
• Asymptotic expansions of certain q-series and a formula of Ramanujan for specific values of the Riemann zeta function
• Rapidly convergent series representations for ζ(2n+1) and their χ-analogue
• Asymptotic expansions of double zeta-functions of Barnes, of Shintani, and Eisenstein series
• On Epstein's Zeta-function.
• COMPLEX FOURIER--BESSEL TRANSFORMS
• On Epstein's Zeta Function (I)