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Compact unitary periods

Published online by Cambridge University Press:  26 March 2007

Erez Lapid  and
Omer Offen
Erez Lapid
Affiliation:
Institute of Mathematics, The Hebrew University of Jerusalem, Jerusalem 91904, Israel erezla@math.huji.ac.il
Omer Offen
Affiliation:
Humboldt-Universität zu Berlin, Institut für Mathematik, Rudower Chaussee 25, D-10099 Berlin, Germany offen@mathematik.hu-berlin.de
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Abstract

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Let $E$ be a $\textrm{CM}$-field and $\pi$ a cuspidal representation of $\textrm{GL}_n({\mathbb{A}}_E)$ which admits a spherical vector (at all places) <formula form="inline" disc="math" id="ffm005"><formtex notation="AMSTeX">$\phi_0$. We evaluate the period of $\phi_0$ with respect to any compact unitary group. The result is consistent with a conjecture of Sarnak.

Keywords

$L$-functionsperiodsunitary groupsrelative trace formula11F7211F6711F70
Type
Research Article
Information
Compositio Mathematica , Volume 143 , Issue 2 , March 2007 , pp. 323 - 338
Copyright
Foundation Compositio Mathematica 2007