ENGLISH

Explicit Formulas for Regularized Products and Series

By Serge Lang , Jay Jorgenson , Dorian Goldfeld (auth.)

Book information

Publisher
Springer-Verlag Berlin Heidelberg
Year
1994
ISBN
9783540586739, 3-540-58673-3, 0387586733
DOI
10.1007/BFb0074039
LCC
QA3 .L28 no. 1593,QA241 .L28 no. 1593
Open Library ID
OL1113822M
Language
english
Format
PDF
Filesize
5 MB (4738870 bytes)
Series
Lecture Notes in Mathematics 1593
Edition
1
Pages
160\156
Library
mexmat
Time added
2009-07-20 03:45:11
Lie Groups; Differential Geometry; AnalysisNumber Theory; Topological Groups

Description

The theory of explicit formulas for regularized products and series forms a natural continuation of the analytic theory developed in LNM 1564. These explicit formulas can be used to describe the quantitative behavior of various objects in analytic number theory and spectral theory. The present book deals with other applications arising from Gaussian test functions, leading to theta inversion formulas and corresponding new types of zeta functions which are Gaussian transforms of theta series rather than Mellin transforms, and satisfy additive functional equations. Their wide range of applications includes the spectral theory of a broad class of manifolds and also the theory of zeta functions in number theory and representation theory. Here the hyperbolic 3-manifolds are given as a significant example.

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