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

Masao Tsuzuki (Autor)

Buch | Softcover

129 Seiten

2015
American Mathematical Society (Verlag)
978-1-4704-1019-3 (ISBN)

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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.

Masao Tsuzuki, Sophia University, Tokyo, Japan.

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

Reihe/Serie	Memoirs of the American Mathematical Society
Verlagsort	Providence
Sprache	englisch
Maße	178 x 254 mm
Gewicht	217 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Algebra
	Mathematik / Informatik ► Mathematik ► Analysis
	Mathematik / Informatik ► Mathematik ► Arithmetik / Zahlentheorie
ISBN-10	1-4704-1019-2 / 1470410192
ISBN-13	978-1-4704-1019-3 / 9781470410193
Zustand	Neuware