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Large values of Dirichlet L-functions at zeros of a class of L-functions

Part of: Zeta and $L$-functions: analytic theory Polynomials and matrices

Published online by Cambridge University Press:  01 July 2020

Junxian Li
Junxian Li*
Affiliation:
Max Planck Institute for Mathematics, Bonn, Germany
*
e-mail: jli135@mpim-bonn.mpg.de
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Abstract

In this paper, we are interested in obtaining large values of Dirichlet L-functions evaluated at zeros of a class of L-functions, that is,

$$ \begin{align*}\max_{\substack{F(\rho)=0\\ T\leq \Im \rho \leq 2T}}L(\rho,\chi), \end{align*} $$
where $\chi $ is a primitive Dirichlet character and F belongs to a class of L-functions. The class we consider includes L-functions associated with automorphic representations of $GL(n)$ over ${\mathbb {Q}}$.

Keywords

L-functionslarge valueszeros

MSC classification

Primary: 11M06: $zeta (s)$ and $L(s, chi)$
Secondary: 11M26: Nonreal zeros of $zeta (s)$ and $L(s, chi)$; Riemann and other hypotheses 11C20: Matrices, determinants

Information

Type
Article
Information
Canadian Journal of Mathematics , Volume 73 , Issue 6 , December 2021 , pp. 1459 - 1505
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Copyright
© Canadian Mathematical Society 2020

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