Memoirs of the American Mathematical Society 2014; 129 pp; softcover Volume: 235 ISBN10: 1470410192 ISBN13: 9781470410193 List Price: US$81 Individual Members: US$48.60 Institutional Members: US$64.80 Order Code: MEMO/235/1110
Not yet published. Expected publication date is May 1, 2015.
 Starting with Green's functions on adele points of \(\mathrm{GL}(2)\) 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 squarefree level. Table of Contents  Introduction
 Preliminaries
 Preliminary analysis
 Green's functions on \(\mathrm{GL}(2,\mathbb{R})\)
 Green's functions on \(\mathrm{GL}(2,F_v)\) 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
