The exponential-type generating function of the Riemann zeta-function revisited
type: Item
instance of: scholarly article
title: The exponential-type generating function of the Riemann zeta-function revisited
author: Takumi Noda
published in: The Ramanujan Journal
publication date: 2023-01-17T00:00:00Z
review text: In the paper under review, the author introduces Dirichlet series associated with the Poincaré series attached to \(\mathrm{SL}(2, \mathbb{Z})\). In this work, certain integral representations and transformation formulas are presented, that describe the Voronoï-type summation formula for the exponential-type generating function of the Riemann zeta-function. In the form of application, the author establishes a new proof of the Fourier series expansion of holomorphic Poincaré series.
Mathematics Subject Classification ID: 11M41
Mathematics Subject Classification ID: 11F11
zbMATH DE Number: 7643070
zbMATH Keywords: generating function
zbMATH Keywords: Riemann zeta-function
zbMATH Keywords: holomorphic Poincaré series
reviewed by: Michael Th. Rassias
MaRDI profile type: Publication
full work available at URL: s11139-022-00644-7
OpenAlex ID: W4304606475
Wikidata QID: Q115602862
cites work: Character analogues of the Poisson and Euler-MacLaurin summation formulas with applications
cites work: Asymptotic behavior of some power series with \(\zeta\)-functions in the coefficients
cites work: Q5719547
cites work: Q5820721
cites work: Notes on the Theory of Series (XX): On Lambert Series
cites work: Q4137395
cites work: On the structure of the Selberg class. I: \(0\leq d\leq 1\).
cites work: On the structure of the Selberg class, VI: non-linear twists
cites work: A Note on Bessel Twists of L-Functions
cites work: Twists and resonance of \(L\)-functions. I.
cites work: Q4168977
cites work: Q4378272
cites work: Asymptotic approximations to the Hardy-Littlewood function
cites work: On the functional properties of Bessel zeta-functions
cites work: On the functional properties of the confluent hypergeometric zeta-function
cites work: Some generating functions of the Riemann zeta function
cites work: On ∑ 1/N sin(x/n )
DOI: 10.1007/S11139-022-00644-7
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description: scientific article; zbMATH DE number 7643070