Isolation of cuspidal spectrum, with application to the Gan–Gross–Prasad conjecture

Raphaël Beuzart-Plessis; Yifeng Liu; Wei Zhang; Xinwen Zhu

doi:10.4007/annals.2021.194.2.5

Isolation of cuspidal spectrum, with application to the Gan–Gross–Prasad conjecture

Raphaël Beuzart-Plessis
, Yifeng Liu
, Wei Zhang
, Xinwen Zhu

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

Abstract

We introduce a new technique for isolating components on the spectral side of the trace formula. By applying it to the Jacquet–Rallis relative trace formula, we complete the proof of the global Gan–Gross–Prasad conjecture and its refinement Ichino–Ikeda conjecture for U(n) X U(n + 1) in the stable case.

Original language	English
Pages (from-to)	519-584
Number of pages	66
Journal	Annals of Mathematics
Volume	194
Issue number	2
DOIs	https://doi.org/10.4007/annals.2021.194.2.5
Publication status	Published - 1 Sept 2021
Externally published	Yes

Keywords

Cuspidal automorphic representations
Gan–gross–prasad conjecture
Isolation of spectrum
Multipliers
Trace formula

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10.4007/annals.2021.194.2.5

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abstract = "We introduce a new technique for isolating components on the spectral side of the trace formula. By applying it to the Jacquet–Rallis relative trace formula, we complete the proof of the global Gan–Gross–Prasad conjecture and its refinement Ichino–Ikeda conjecture for U(n) X U(n + 1) in the stable case.",

keywords = "Cuspidal automorphic representations, Gan–gross–prasad conjecture, Isolation of spectrum, Multipliers, Trace formula",

author = "Rapha{\"e}l Beuzart-Plessis and Yifeng Liu and Wei Zhang and Xinwen Zhu",

note = "Publisher Copyright: {\textcopyright} 2021. Department of Mathematics, Princeton University.",

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T1 - Isolation of cuspidal spectrum, with application to the Gan–Gross–Prasad conjecture

AU - Beuzart-Plessis, Raphaël

AU - Liu, Yifeng

AU - Zhang, Wei

AU - Zhu, Xinwen

PY - 2021/9/1

Y1 - 2021/9/1

N2 - We introduce a new technique for isolating components on the spectral side of the trace formula. By applying it to the Jacquet–Rallis relative trace formula, we complete the proof of the global Gan–Gross–Prasad conjecture and its refinement Ichino–Ikeda conjecture for U(n) X U(n + 1) in the stable case.

AB - We introduce a new technique for isolating components on the spectral side of the trace formula. By applying it to the Jacquet–Rallis relative trace formula, we complete the proof of the global Gan–Gross–Prasad conjecture and its refinement Ichino–Ikeda conjecture for U(n) X U(n + 1) in the stable case.

KW - Cuspidal automorphic representations

KW - Gan–gross–prasad conjecture

KW - Isolation of spectrum

KW - Multipliers

KW - Trace formula

UR - https://www.scopus.com/pages/publications/85129864560

U2 - 10.4007/annals.2021.194.2.5

DO - 10.4007/annals.2021.194.2.5

M3 - Article

AN - SCOPUS:85129864560

SN - 0003-486X

VL - 194

SP - 519

EP - 584

JO - Annals of Mathematics

JF - Annals of Mathematics

IS - 2

ER -

Isolation of cuspidal spectrum, with application to the Gan–Gross–Prasad conjecture

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Keywords

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