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Fourier transforms related to ζ(s)

Part of: Zeta and $L$-functions: analytic theory Harmonic analysis in one variable

Published online by Cambridge University Press:  30 April 2021

Pablo A. Panzone
Pablo A. Panzone*
Affiliation:
Departamento e Instituto de Matematica, Universidad Nacional del Sur, Av. Alem 1253, 8000Bahia Blanca, Argentina (pablopanzone@hotmail.com)
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Abstract

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Using some formulas of S. Ramanujan, we compute in closed form the Fourier transform of functions related to Riemann zeta function $\zeta (s)=\sum \nolimits _{n=1}^{\infty } {1}/{n^{s}}$ and other Dirichlet series.

Keywords

Fourier transformDirichlet Seriesintegralssupported in part by UNS and CONICET

MSC classification

Primary: 42A38: Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type
Secondary: 11M99: None of the above, but in this section
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 64 , Issue 2 , May 2021 , pp. 200 - 216
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Copyright
Copyright © The Author(s), 2021. Published by Cambridge University Press on Behalf of The Edinburgh Mathematical Society

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