Top Fourier coefficients of residual Eisenstein series on symplectic or metaplectic groups, induced from Speh representations

David Ginzburg; David Soudry

doi:10.1007/s40993-021-00306-5

Top Fourier coefficients of residual Eisenstein series on symplectic or metaplectic groups, induced from Speh representations

David Ginzburg, David Soudry

School of Mathematical Sciences

Tel Aviv University

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

Abstract

We consider the residues at the poles in the half plane Re(s) ≥ 0 of Eisenstein series, on symplectic groups, or their double covers, induced from Speh representations. We show that for each such pole, there is a unique maximal nilpotent orbit, attached to Fourier coefficients admitted by the corresponding residual representation. We find this orbit in each case.

Original language	English
Article number	10
Journal	Research in Number Theory
Volume	8
Issue number	1
DOIs	https://doi.org/10.1007/s40993-021-00306-5
State	Published - Mar 2022

Keywords

Eisenstein series
Nilpotent orbits
Poles
Speh representations

All Science Journal Classification (ASJC) codes

Algebra and Number Theory

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10.1007/s40993-021-00306-5

Cite this

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title = "Top Fourier coefficients of residual Eisenstein series on symplectic or metaplectic groups, induced from Speh representations",

abstract = "We consider the residues at the poles in the half plane Re(s) ≥ 0 of Eisenstein series, on symplectic groups, or their double covers, induced from Speh representations. We show that for each such pole, there is a unique maximal nilpotent orbit, attached to Fourier coefficients admitted by the corresponding residual representation. We find this orbit in each case.",

keywords = "Eisenstein series, Nilpotent orbits, Poles, Speh representations",

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year = "2022",

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T1 - Top Fourier coefficients of residual Eisenstein series on symplectic or metaplectic groups, induced from Speh representations

AU - Ginzburg, David

AU - Soudry, David

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N2 - We consider the residues at the poles in the half plane Re(s) ≥ 0 of Eisenstein series, on symplectic groups, or their double covers, induced from Speh representations. We show that for each such pole, there is a unique maximal nilpotent orbit, attached to Fourier coefficients admitted by the corresponding residual representation. We find this orbit in each case.

AB - We consider the residues at the poles in the half plane Re(s) ≥ 0 of Eisenstein series, on symplectic groups, or their double covers, induced from Speh representations. We show that for each such pole, there is a unique maximal nilpotent orbit, attached to Fourier coefficients admitted by the corresponding residual representation. We find this orbit in each case.

KW - Eisenstein series

KW - Nilpotent orbits

KW - Poles

KW - Speh representations

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U2 - 10.1007/s40993-021-00306-5

DO - 10.1007/s40993-021-00306-5

M3 - مقالة

SN - 2363-9555

VL - 8

JO - Research in Number Theory

JF - Research in Number Theory

IS - 1

M1 - 10

ER -

Top Fourier coefficients of residual Eisenstein series on symplectic or metaplectic groups, induced from Speh representations

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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