Local integral transforms and global spectral decomposition

Abstract

We establish an explicit global spectral decomposition of shifted convolution sums and the second moment of automorphic $L$-functions for Maass forms with explicit integral transforms as well as explicit inversion formulae over every local field.

Minor update, to appear in Geom. Funct. Anal. (GAFA)

References in corpus (4)

• Formule de Plancherel pour les fonctions de Whittaker sur un groupe réductif $p$-adique
• The Weyl bound for triple product L-functions
• Motohashi's Formula for the Fourth Moment of Individual Dirichlet $L$-Functions and Applications
• Spectral Moment Formulae for $GL(3)\times GL(2)$ $L$-functions III: The Twisted Case

Cited by in corpus (2)

• Asymptotic Analysis and Phase Transition of the Bessel-Kuznetsov Transform with an Oscillatory Phase
• Spectral Moment Formulae for $GL(3)\times GL(2)$ $L$-functions II: The Eisenstein Case