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

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.

arXiv comment15 pages, revision based on suggestions by referee

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