Groups acting on hyperbolic space
Subtitle: harmonic analysis and number theory
By: J. Elstrodt, F. Grunewald, J. Mennicke.
Contributors: Grunewald, F. 1949-; Mennicke, J. L.
Series: Springer monographs in mathematics
Publisher: Springer
Published: 1998
Place of publication: Berlin; New York
Language: eng
Number of pages: 524
Subjects: Spectral theory (Mathematics); Selberg trace formula; Automorphic forms; Functions, Zeta
Description: 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 of quadratic integers, their Eisenstein series and their associated Hermitian forms. A comprehensive chapter on concrete examples of arithmetic and non-arithmetic cofinite groups enhances the usefulness of this work for a wide audience of mathematicians.
Notes: Includes bibliographical references (p. [497]-520) and index.