Kamel Mazhouda

Affiliation: Universite de Monastir, Tunisia

Email: Kamel.Mazhouda@fsm.rnu.tn

Title Of Talk: Relations equivalent to the generalized Riemann hypothesis for a class of $L$-functions

Abstract: In this talk, we prove that the Generalized Riemann Hypothesis (GRH) for functions in the class ${\mathcal{S}^{\sharp\flat}}$ containing the Selberg class is equivalent to a certain integral expression of the real part of the generalized Li coefficient $\lambda_F(n)$ associated to $F\in{\mathcal{S}^{\sharp\flat}}$, for positive integers $n$. Moreover, we deduce that the GRH is equivalent to a certain expression of $\mbox{Re}(\lambda_F(n))$ in terms of the sum of the Chebyshev polynomials of the first kind. Then, we partially evaluate the integral expression and deduce further relations equivalent to the GRH involving the generalized Euler-Stieltjes constants of the second kind associated to $F$. This is joint work with Lejla Smajlović, University of Sarajevo.

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