The exponential-type generating function of the Riemann zeta-function revisited

Dirichlet series associated with the Poincaré series attached to SL ( 2 , Z ) are introduced. Integral representations and transformation formulas are given, which describe the Voronoï-type summation formula for the exponential-type generating function of the Riemann zeta-function. As an application...

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Bibliographic Details
Published in:The Ramanujan journal 2023-01, Vol.60 (1), p.1-11
Main Author: Noda, Takumi
Format: Article
Language:English
Subjects:
Combinatorics
Dirichlet problem
Field Theory and Polynomials
Fourier Analysis
Fourier series
Functions of a Complex Variable
Mathematics
Mathematics and Statistics
Number Theory
Series expansion
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Summary:Dirichlet series associated with the Poincaré series attached to SL ( 2 , Z ) are introduced. Integral representations and transformation formulas are given, which describe the Voronoï-type summation formula for the exponential-type generating function of the Riemann zeta-function. As an application, a new proof of the Fourier series expansion of holomorphic Poincaré series is given.
ISSN:1382-4090
1572-9303
DOI:10.1007/s11139-022-00644-7