ENGLISH

Kuznetsov's trace formula and the Hecke eigenvalues of Maass forms

By Li C. , Knightly A.

Book information

Publisher
Amer Mathematical Society
Year
2013
ISBN
0821887440, 978-0-8218-8744-8
Language
english
Format
PDF
Filesize
1 MB (1362028 bytes)
Series
Memoirs of the American Mathematical Society 1055
Pages
144\144
Library
kolxoz
Time added
2015-12-12 14:00:00

Description

The authors give an adelic treatment of the Kuznetsov trace formula as a relative trace formula on $\operatorname{GL}(2)$ over $\mathbf{Q}$. The result is a variant which incorporates a Hecke eigenvalue in addition to two Fourier coefficients on the spectral side. The authors include a proof of a Weil bound for the generalized twisted Kloosterman sums which arise on the geometric side. As an application, they show that the Hecke eigenvalues of Maass forms at a fixed prime, when weighted as in the Kuznetsov formula, become equidistributed relative to the Sato-Tate measure in the limit as the level goes to infinity

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