Periods and global invariants of automorphic representations

Joseph Bernstein; Andre Reznikov

doi:10.1016/j.jnt.2022.07.010

Periods and global invariants of automorphic representations

Joseph Bernstein
, Andre Reznikov

Tel Aviv University, Bar-Ilan University

Research output: Contribution to journal › Article › peer-review

Abstract

We consider periods of automorphic representations of adele groups defined by integrals along Gelfand subgroups. We define natural maps between local components of such periods and construct corresponding global maps using automorphic L-functions. This leads to an introduction of a global invariant of an automorphic representation arising from two such periods. We compute this invariant in some cases.

Original language	English
Pages (from-to)	117-159
Number of pages	43
Journal	Journal of Number Theory
Volume	243
DOIs	https://doi.org/10.1016/j.jnt.2022.07.010
State	Published - Feb 2023

Keywords

Automorphic representations
Co-invariants
L-functions
Periods

ASJC Scopus subject areas

Algebra and Number Theory

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10.1016/j.jnt.2022.07.010

Cite this

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title = "Periods and global invariants of automorphic representations",

abstract = "We consider periods of automorphic representations of adele groups defined by integrals along Gelfand subgroups. We define natural maps between local components of such periods and construct corresponding global maps using automorphic L-functions. This leads to an introduction of a global invariant of an automorphic representation arising from two such periods. We compute this invariant in some cases.",

keywords = "Automorphic representations, Co-invariants, L-functions, Periods",

author = "Joseph Bernstein and Andre Reznikov",

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doi = "10.1016/j.jnt.2022.07.010",

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AU - Bernstein, Joseph

AU - Reznikov, Andre

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N2 - We consider periods of automorphic representations of adele groups defined by integrals along Gelfand subgroups. We define natural maps between local components of such periods and construct corresponding global maps using automorphic L-functions. This leads to an introduction of a global invariant of an automorphic representation arising from two such periods. We compute this invariant in some cases.

AB - We consider periods of automorphic representations of adele groups defined by integrals along Gelfand subgroups. We define natural maps between local components of such periods and construct corresponding global maps using automorphic L-functions. This leads to an introduction of a global invariant of an automorphic representation arising from two such periods. We compute this invariant in some cases.

KW - Automorphic representations

KW - Co-invariants

KW - L-functions

KW - Periods

UR - https://www.scopus.com/pages/publications/85139274107

U2 - 10.1016/j.jnt.2022.07.010

DO - 10.1016/j.jnt.2022.07.010

M3 - Article

SN - 0022-314X

VL - 243

SP - 117

EP - 159

JO - Journal of Number Theory

JF - Journal of Number Theory

ER -

Periods and global invariants of automorphic representations

Abstract

Keywords

ASJC Scopus subject areas

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