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March 2020 On the linear twist of degree $1$ functions in the extended Selberg class
Giamila Zaghloul
Funct. Approx. Comment. Math. 62(1): 105-120 (March 2020). DOI: 10.7169/facm/1801

Abstract

Given a degree 1 function $F\in\mathcal{S}^{\sharp}$ and a real number $\alpha$, we consider the linear twist $F(s,\alpha)$, proving that it satisfies a functional equation reflecting $s$ into $1-s$, which can be seen as a Hurwitz-Lerch type of functional equation. We also derive some results on the distribution of the zeros of the linear twist.

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Giamila Zaghloul. "On the linear twist of degree $1$ functions in the extended Selberg class." Funct. Approx. Comment. Math. 62 (1) 105 - 120, March 2020. https://doi.org/10.7169/facm/1801

Information

Published: March 2020
First available in Project Euclid: 26 October 2019

zbMATH: 07225503
MathSciNet: MR4074391
Digital Object Identifier: 10.7169/facm/1801

Subjects:
Primary: 11M41

Rights: Copyright © 2020 Adam Mickiewicz University

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Vol.62 • No. 1 • March 2020
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