Complete asymptotic expansions associated with Epstein zeta-functions. II
type: Item
instance of: scholarly article
title: Complete asymptotic expansions associated with Epstein zeta-functions. II
zbMATH Open document ID: 1322.11031
author: Masanori Katsurada
published in: The Ramanujan Journal
publication date: 2015-03-24T00:00:00Z
review text: Let \(s=\sigma+it\) be a complex variable, \(\sigma>1\), \(z=x+iy\) a complex parameter in the upper half-plane, \(a, b, \mu,\) and \(\nu\) real parameters, \(Q(u,v)\) a real positive-definite quadratic form. The author studies the corresponding generalized Epstein zeta function attached to the form \(Q\), in the case the quadratic form \(Q=|u+vz|^2\). Namely, he studies the asymptotic aspects of the zeta function when \(y\rightarrow+\infty\) and \(z\rightarrow0\) through the sector \(0<\)arg\(z<\pi\) and also studies definite asymptotic aspects of the Riemann-Liouville transform of the zeta function constructed in a particular case. For Part I see [ibid. 14, No. 2, 249--275 (2007; Zbl 1171.11023)].
reviewed by: Guram Gogishvili
Mathematics Subject Classification ID: 11E45
Mathematics Subject Classification ID: 11F11
Mathematics Subject Classification ID: 11M35
zbMATH DE Number: 6418841
zbMATH Keywords: Epstein zeta-function
zbMATH Keywords: Mellin-Barnes integral
zbMATH Keywords: asymptotic expansion
zbMATH Keywords: weighted mean value
zbMATH Keywords: Riemann-Liouville transform
MaRDI profile type: Publication
full work available at URL: s11139-014-9583-6
OpenAlex ID: W4236958427
cites work: On the Lerch zeta function
cites work: Q5485643
cites work: On Epstein's Zeta Function (I)
cites work: On Epstein's Zeta-function.
cites work: Q5820721
cites work: Q5824493
cites work: On a formula of Hecke
cites work: Q3220660
cites work: Power series with the Riemann zeta-function in the coefficients
cites work: An application of Mellin-Barnes' type integrals to the mean square of Lerch zeta-functions
cites work: Q4378272
cites work: An application of the Mellin-Barnes type of integral to the mean square of \(L\)-functions
cites work: Power series and asymptotic series associated with the Lerch zeta-function
cites work: Rapidly convergent series representations for ζ(2n+1) and their χ-analogue
cites work: On an asymptotic formula of Ramanujan for a certain theta-type series
cites work: Asymptotic expansions of certain q-series and a formula of Ramanujan for specific values of the Riemann zeta function
cites work: An application of Mellin-Barnes type integrals to the mean square of Lerch zeta-functions. II
cites work: Complete asymptotic expansions associated with Epstein zeta-functions
cites work: Asymptotic expansions for double Shintani zeta-functions of several variables
cites work: Complete asymptotic expansions for certain multiple q-integrals and q-differentials of Thomae–Jackson type
cites work: DIFFERENTIAL ACTIONS ON THE ASYMPTOTIC EXPANSIONS OF NON-HOLOMORPHIC EISENSTEIN SERIES
cites work: ON CHARACTERISTIC TWISTS OF CERTAIN DIRICHLET SERIES
cites work: Asymptotic expansions of double zeta-functions of Barnes, of Shintani, and Eisenstein series
cites work: Q5164805
cites work: Q3934463
cites work: Q3259158
cites work: L-functions and character sums for quadratic forms (I)
cites work: Functional Equations of Generalized Epstein Zeta Functions in Several Complex Variables
DOI: 10.1007/S11139-014-9583-6
description: scientific article; zbMATH DE number 6418841