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ON THE FIRST OCCURRENCE OF CUSPIDAL REPRESENTATIONS OF SYMPLECTIC GROUPS

Published online by Cambridge University Press:  03 November 2005

David Ginzburg  and
Nadya Gurevich
David Ginzburg
Affiliation:
School of Mathematics, Tel-Aviv University, Ramat Aviv, Tel Aviv 69978, Israel (ginzburg@post.tau.ac.il)
Nadya Gurevich
Affiliation:
School of Mathematics, Ben Gurion University of the Negev, PO Box 653, Be’er Sheva 84105, Israel (ngur@cs.bgu.ac.il)
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Abstract

We study the first occurrence of a cuspidal representation $\pi$ of $\mathrm{Sp}_{2n}(\mathbb{A})$ in the tower of split orthogonal groups under symplectic-orthogonal theta lift. We give upper and lower bounds for the first occurrence in terms of the wave front of $\pi$. Besides we describe a class of small cuspidal representations whose first occurrence is the maximal possible.

Keywords

first occurrencewave frontFourier coefficients of automorphic formsPrimary 11F7011F30
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 5 , Issue 1 , January 2006 , pp. 35 - 52
Copyright
2005 Cambridge University Press

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