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Explicit Formulas for Regularized Products and Series

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...

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Bibliographic Details
Main Authors: Jorgenson, Jay, Lang, Serge (Author), Goldfeld, Dorian (Author)
Format: eBook
Language:English
Published: Berlin, Heidelberg Springer Berlin Heidelberg 1994, 1994
Edition:1st ed. 1994
Series:Lecture Notes in Mathematics
Subjects:
Number Theory
Geometry, Differential
Mathematical Analysis
Topological Groups And Lie Groups
Lie Groups
Topological Groups
Analysis
Differential Geometry
Online Access:
Collection: Springer Book Archives -2004 - Collection details see MPG.ReNa
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520 |a 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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