Explicit Formulas: for Regularized Products and Series
Author:   Dorian Goldfeld ,  Jay Jorgenson ,  Serge Lang ,  Dorian Goldfeld
Publisher:   Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Edition:   1994 ed.
Volume:   1593
ISBN:  

9783540586739


Pages:   160
Publication Date:   16 December 1994
Format:   Paperback
Availability:   In Print   Availability explained
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Explicit Formulas: for Regularized Products and Series


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Overview

The theory of explicit formulae for regularized products and series forms a natural continuation of the analytic theory developed in LNM 1564. These explicit formulae can be used to describe the quantitative behaviour 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 formulae 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 ad representation theory. Here, the hyperbolic 3-manifolds are given as a significant example.

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