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

Journal Article (2025)
Author(s)

Felipe Gonçalves (Instituto Nacional de Matemática Pura e Aplicada - IMPA)

David de Laat (TU Delft - Discrete Mathematics and Optimization)

N.M. Leijenhorst (TU Delft - Discrete Mathematics and Optimization)

Research Group
Discrete Mathematics and Optimization
DOI related publication
https://doi.org/10.1090/mcom/4005
More Info
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Publication Year
2025
Language
English
Research Group
Discrete Mathematics and Optimization
Bibliographical Note
Green Open Access added to TU Delft Institutional Repository as part of the Taverne amendment. More information about this copyright law amendment can be found at https://www.openaccess.nl. Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.@en
Issue number
354
Volume number
94
Pages (from-to)
2041-2058
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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 GLm/Q. For this, we apply the higher-level correlation asymptotic of Hejhal, Rudnick, and Sarnak in conjunction with semidefinite programming bounds.

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