Explicit Formulas: for Regularized Products and Series / Edition 1

by Jay Jorgenson, Serge Lang, Dorian Goldfeld

Overview

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.

Product Details

ISBN-13:	9783540586739
Publisher:	Springer Berlin Heidelberg
Publication date:	12/27/1994
Series:	Lecture Notes in Mathematics , #1593
Edition description:	1994
Pages:	160
Product dimensions:	6.10(w) x 9.25(h) x 0.01(d)

Table of Contents

Explicit formulas for regularized products and series.- A spectral interpretation of Weil's explicit formula.