Spectral Means of Central Values of Automorphic $L$-Functions for GL(2)

ISBN-13: 9781470410193 / Angielski

Masao Tsuzuki

Opis

Starting with Green's functions on adele points of $mathrm(2)$ considered over a totally real number field, the author elaborates an explicit version of the relative trace formula, whose spectral side encodes the informaton on period integrals of cuspidal waveforms along a maximal split torus. As an application, he proves two kinds of asymptotic mean formula for certain central $L$-values attached to cuspidal waveforms with square-free level.

Spis treści

• Introduction
• Preliminaries
• Preliminary analysis
• Green's functions on $\mathrm(2,\mathbb)$
• Green's functions on $\mathrm(2,F_v)$ with $v$ a non archimedean place
• Kernel functions
• Regularized periods
• Automorphic Green's functions
• Automorphic smoothed kernels
• Periods of regularized automorphic smoothed kernels: the spectral side
• A geometric expression of automorphic smoothed kernels
• Periods of regularized automorphic smoothed kernels: the geometric side
• Asymptotic formulas
• An error term estimate in the Weyl type asymptotic law
• Appendix
• Bibliography