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arXiv · 2303.01095

Multiplicity of nontrivial zeros of primitive L-functions via higher-level correlations

Felipe Gonçalves·David de Laat·Nando Leijenhorst
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Abstract

We give universal bounds on the fraction of nontrivial zeros having given multiplicity for L-functions attached to a cuspidal automorphic representation of $\mathrm{GL}_m/\mathbb{Q}$. For this, we apply the higher-level correlation asymptotic of Hejhal and Rudnick & Sarnak in conjunction with semidefinite programming bounds.

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Felipe Gonçalves, David de Laat, Nando Leijenhorst. 2023-03-02. Multiplicity of nontrivial zeros of primitive L-functions via higher-level correlations. https://doi.org/10.1090/mcom/4005

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