Spectral means of central values of automorphic L-functions for GL(2)
著者
書誌事項
Spectral means of central values of automorphic L-functions for GL(2)
(Memoirs of the American Mathematical Society, no. 1110)
American Mathematical Society, 2015, c2014
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注記
"Volume 235, number 1110 (fifth of 5 numbers), May 2015"
Includes bibliographical references (p. 127-129)
内容説明・目次
内容説明
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.
目次
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
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