Multiplicity one theorems for the generalized doubling method

Dmitry Gourevitch; Eyal Kaplan; Avraham Aizenbud; Dmitry Gourevitch

doi:10.4171/JEMS/1207

Multiplicity one theorems for the generalized doubling method

Dmitry Gourevitch, Eyal Kaplan, Avraham Aizenbud, Dmitry Gourevitch

Weizmann Institute of Science, Bar-Ilan University, Tel Aviv University

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

Abstract

We prove the local multiplicity at most one theorem underlying the definition and theory of local -, ∊- and L-factors, defined by virtue of the generalized doubling method, over any local field of characteristic 0. We also present two applications: one to the existence of local factors for genuine representations of covering groups, the other to the global unfolding argument of the doubling integral.

Original language	English
Pages (from-to)	3007-3092
Number of pages	86
Journal	Journal of the European Mathematical Society
Volume	25
Issue number	8
DOIs	https://doi.org/10.4171/JEMS/1207
State	Published - 2023

Keywords

Doubling method
Schwartz functions
covering groups
invariant distributions
multiplicity one

All Science Journal Classification (ASJC) codes

General Mathematics
Applied Mathematics

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10.4171/JEMS/1207

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title = "Multiplicity one theorems for the generalized doubling method",

abstract = "We prove the local multiplicity at most one theorem underlying the definition and theory of local -, ∊- and L-factors, defined by virtue of the generalized doubling method, over any local field of characteristic 0. We also present two applications: one to the existence of local factors for genuine representations of covering groups, the other to the global unfolding argument of the doubling integral.",

keywords = "Doubling method, Schwartz functions, covering groups, invariant distributions, multiplicity one",

author = "Dmitry Gourevitch and Eyal Kaplan and Avraham Aizenbud and Dmitry Gourevitch",

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year = "2023",

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AU - Kaplan, Eyal

AU - Aizenbud, Avraham

AU - Gourevitch, Dmitry

PY - 2023

Y1 - 2023

N2 - We prove the local multiplicity at most one theorem underlying the definition and theory of local -, ∊- and L-factors, defined by virtue of the generalized doubling method, over any local field of characteristic 0. We also present two applications: one to the existence of local factors for genuine representations of covering groups, the other to the global unfolding argument of the doubling integral.

AB - We prove the local multiplicity at most one theorem underlying the definition and theory of local -, ∊- and L-factors, defined by virtue of the generalized doubling method, over any local field of characteristic 0. We also present two applications: one to the existence of local factors for genuine representations of covering groups, the other to the global unfolding argument of the doubling integral.

KW - Doubling method

KW - Schwartz functions

KW - covering groups

KW - invariant distributions

KW - multiplicity one

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DO - 10.4171/JEMS/1207

M3 - مقالة

SN - 1435-9855

VL - 25

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EP - 3092

JO - Journal of the European Mathematical Society

JF - Journal of the European Mathematical Society

IS - 8

ER -

Multiplicity one theorems for the generalized doubling method

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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