Theta correspondence and simple factors in global Arthur parameters

Wu, Chenyan

doi:10.2140/ant.2024.18.969

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Theta correspondence and simple factors in global Arthur parameters

Chenyan Wu

Vol. 18 (2024), No. 5, 969–991

DOI: 10.2140/ant.2024.18.969

Abstract

By using results on poles of $L$ -functions and theta correspondence, we give a bound on $b$ for $(χ, b)$ -factors of the global Arthur parameter of a cuspidal automorphic representation $π$ of a classical group or a metaplectic group where $χ$ is a conjugate self-dual automorphic character and $b$ is an integer which is the dimension of an irreducible representation of ${SL}_{2} (ℂ)$ . We derive a more precise relation when $π$ lies in a generic global $A$ -packet.

Keywords

theta correspondence, Eisenstein series, $L$-functions, Arthur parameters

Mathematical Subject Classification

Primary: 11F27, 11F67, 11F70

Milestones

Received: 30 August 2022

Revised: 3 May 2023

Accepted: 20 July 2023

Published: 16 April 2024

Authors

Chenyan Wu
School of Mathematics and Statistics University of Melbourne Melbourne Victoria Australia

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Vol. 18, No. 5, 2024