Spectral Means of Central Values of Automorphic $l$-functions for Gl2 (Memoirs of the American Mathematical Society)
Author： Masao Tsuzuki
Publisher： American Mathematical Society
Publication year： 2015
E-ISBN: 9781470422288
P-ISBN(Paperback): 9781470410193
P-ISBN(Hardback): 9781470410193
Subject： O174.54 elliptic function, the Abel function, automorphic function
Keyword： Number Theory
Language： ENG
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Spectral Means of Central Values of Automorphic $l$-functions for Gl2 (Memoirs of the American Mathematical Society)
Description
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 square-free level.