Kuznetsov's Trace Formula and the Hecke Eigenvalues of Maass Forms (eBook)

Andrew H Knightly (Autor)

eBook Download: PDF

132 Seiten
American Mathematical Society (Verlag)
978-1-4704-1006-3 (ISBN)

Infos

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.

Produkt-Details

• Themenwelt: Mathematik / Informatik ► Mathematik ► Arithmetik / Zahlentheorie
• ISBN-10: 1-4704-1006-0 / 1470410060
• ISBN-13: 978-1-4704-1006-3 / 9781470410063