Explicit Formulas

For Regularized Products and Series

By: Jay Jorgenson, Serge Lang, Dorian Goldfeld

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Paperback | 16 December 1994

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168 Pages

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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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Explicit Formulas for Regularized Products and Series
Asymptotic estimates of regularized harmonic series	p. 11
Cramer's Theorem as an Explicit Formula	p. 43
Explicit Formulas under Fourier Assumptions	p. 61
From Functional Equations to Theta Inversions	p. 85
From Theta Inversions to Functional Equations	p. 97
A Generalization of Fujii's Theorem	p. 119
A Spectral Interpretation of Weil's Explicit Formula
Notation	p. 139
Construction of the indefinite space [actual symbol not reproducible]	p. 140
Spectral theory of [actual symbol not reproducible]	p. 141
Eisenstein series	p. 142
Cusp forms	p. 145
The zeta function associated to an automorphic form on [actual symbol not reproducible]	p. 147
The Rankin-Selberg convolution	p. 148
Higher rank generalizations	p. 148
Index
Table of Contents provided by Blackwell. All Rights Reserved.

Explicit Formulas

For Regularized Products and Series

At a Glance

Paperback

Shipping

How to return your order

Defective items

You Can Find This Book In

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