Rankin-Selberg Integrals and L-Functions for Covering Groups of General Linear Groups

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Abstract

Let GL(m)c be the covering group of GLc, obtained by restriction from the m-fold central extension of Matsumoto of the symplectic group. We introduce a new family of Rankin- Selberg integrals for representations of GL(m)c × GL(m)k. The construction is based on certain assumptions, which we prove here for k = 1. Using the integrals, we define local γ -, L-, and ∈-factors. Globally, our construction is strong in the sense that the integrals are truly Eulerian. This enables us to define the completed L-function for cuspidal representations and prove its standard functional equation.

Original languageEnglish
Pages (from-to)13332-13386
Number of pages55
JournalInternational Mathematics Research Notices
Volume2023
Issue number15
Early online date26 Jul 2022
DOIs
StatePublished - 1 Jul 2023

Bibliographical note

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© The Author(s) 2022.

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