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Kuznetsov's Trace Formula and the Hecke Eigenvalues of Maass Forms: 1055 (Memoirs of the American Mathematical Society)

Mathematical Theory

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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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Format: paperback
ASIN: 0821887440
Category: Books > Subjects > Science, Nature & Maths > Mathematics > Mathematical Theory
Domain: Amazon UK
Release Date: 30 August 2013
Listed Since: 07 June 2013

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Kuznetsov's Trace Formula and the Hecke Eigenvalues of Maass Forms: 1055 (Memoirs of the American Mathematical Society)

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