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Groups Acting on Hyperbolic Space: Harmonic Analysis and Number Theory / Edition 1
     

Groups Acting on Hyperbolic Space: Harmonic Analysis and Number Theory / Edition 1

by Juergen Elstrodt, Fritz Grunewald, Jens Mennicke
 

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ISBN-10: 3642083021

ISBN-13: 9783642083020

Pub. Date: 12/09/2010

Publisher: Springer Berlin Heidelberg

This book deals with a broad range of topics from the theory of automorphic functions on three-dimensional hyperbolic space and its arithmetic group theoretic and geometric ramifications. Starting off with several models of hyperbolic space and its group of motions the authors discuss the spectral theory of the Laplacian and Selberg's theory for cofinite groups.

Overview

This book deals with a broad range of topics from the theory of automorphic functions on three-dimensional hyperbolic space and its arithmetic group theoretic and geometric ramifications. Starting off with several models of hyperbolic space and its group of motions the authors discuss the spectral theory of the Laplacian and Selberg's theory for cofinite groups. This culminates in explicit versions of the Selberg trace formula and the Selberg zeta-function. The interplay with arithmetic is demonstrated by means of the groups PSL(2) over rings and of quadratic integers, their Eisenstein series and their associated Hermitian forms. A rich chapter on concrete examples of arithmetic and non-arithmetic cofinite groups enhances the usefulness of this work for a wide circle of mathematicians.

Product Details

ISBN-13:
9783642083020
Publisher:
Springer Berlin Heidelberg
Publication date:
12/09/2010
Series:
Springer Monographs in Mathematics Series
Edition description:
Softcover reprint of hardcover 1st ed. 1998
Pages:
524
Product dimensions:
1.10(w) x 9.21(h) x 6.14(d)

Table of Contents

1. Three-Dimensional Hyperbolic Space.- 2. Groups Acting Discontinuously on Three-Dimensional Hyperbolic Space.- 3. Automorphic Functions.- 4. Spectral Theory of the Laplace Operator.- 5. Spectral Theory of the Laplace Operator for Cocompact Groups.- 6. Spectral Theory of the Laplace Operator for Cofinite Groups.- 7. PSL(2) over Rings of Imaginary Quadratic Integers.- 8. Eisenstein Series for PSL(2) over Imaginary Quadratic Integers.- 9. Integral Binary Hermitian Forms.- 10. Examples of Discontinuous Groups.- References.

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