Groups acting on hyperbolic space: Harmonic analysis and number theory. Fritz Grunewald, Jens Mennicke, Juergen Elstrodt

Groups acting on hyperbolic space: Harmonic analysis and number theory



Download Groups acting on hyperbolic space: Harmonic analysis and number theory



Groups acting on hyperbolic space: Harmonic analysis and number theory Fritz Grunewald, Jens Mennicke, Juergen Elstrodt ebook djvu
Publisher: Springer
Language: English
Page: 539
ISBN: 3540627456, 9783540627456

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.



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