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Endoscopy and cohomology growth on $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}U(3)$

Part of: Discontinuous groups and automorphic forms

Published online by Cambridge University Press:  24 April 2014

Simon Marshall
Simon Marshall*
Affiliation:
Department of Mathematics, Northwestern University, 2033 Sheridan Road, Evanston, IL 60208, USA email slm@math.northwestern.edu
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Abstract

We apply the endoscopic classification of automorphic forms on $U(3)$ to study the growth of the first Betti number of congruence covers of a Picard modular surface. As a consequence, we establish a case of a conjecture of Sarnak and Xue on cohomology growth.

Keywords

arithmetic groupscohomologyautomorphic formsendoscopy

MSC classification

Secondary: 11F75: Cohomology of arithmetic groups 11F70: Representation-theoretic methods; automorphic representations over local and global fields

Information

Type
Research Article
Information
Compositio Mathematica , Volume 150 , Issue 6 , June 2014 , pp. 903 - 910
Copyright
© The Author 2014 

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