# The Spectral Theory of Geometrically Periodic Hyperbolic 3-Manifolds (Memoirs of the American Mathematical Society) download ebook

## by **Charles L. Epstein**

Memoirs of the American Mathematical Society 1985; 161 pp; MSC: Primary 58; Secondary 1. The Spectral Theory of Geometrically Periodic Hyperbolic 3-Manifolds.

Memoirs of the American Mathematical Society 1985; 161 pp; MSC: Primary 58; Secondary 11. Electronic ISBN: 978-1-4704-0748-3 Product Code: MEMO/58/335. Base Product Code Keyword List: memo; MEMO; memo/58; MEMO/58; memo-58; MEMO-58; memo/58/335; MEMO/58/335; memo-58-335; MEMO-58-335. Online Product Code: MEMO/58/335.

Keywords - Spectral theory on manifolds, trace formulas, lattice point asymptotics, geometrically .

Keywords - Spectral theory on manifolds, trace formulas, lattice point asymptotics, geometrically non-finite groups. Memoirs of the American Mathematical Society, ISSN 0065-9266; no. 335) Corrected version of author's dissertation-New York University, 1983. Bibliography: p. "November 1985, volume 58 number 335 (first of four numbers). 1. Three-manifolds (Topology) 2. Spectral theory (Mathematics) I. Title.

2 Charles L. Epstein 3 The plane y 0 along with the point at (in H ) form the ideal boundary of. .Geometrically non-finite groups can be extremely complicated, and we have restricted outselves to what is perhaps the simplest. Epstein 3 The plane y 0 along with the point at (in H ) form the ideal boundary of hyperbolic 3-space. We will refer to this as the plane at ° °. 3 The group of orientation preserving isometries of H is isomorphic 3 to PSL(2,IC) y1 0. A non-simply connected hyperbolic 3-manifold, M, can be represented o as the quotient of H by a discrete subgroup T of PSL(2,E). The 3 group r is isomorphic to n~ (M). H is the universal covering space of 3 M- H /r and the projection is a local isometry. Geometrically non-finite groups can be extremely complicated, and we have restricted outselves to what is perhaps the simplest subclass of such groups.

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American Mathematical Society: Memoirs of the American . In this paper we develop the spectral theory of the Laplace-Beltrami operator for geometrically periodic hyperbolic 3-manifolds, H3/G.

American Mathematical Society: Memoirs of the American Mathematical Society. Część 335. Charles L. Epstein1 stycznia 1985. American Mathematical Soc. Kup na prezent. Dodaj do listy życzeń. 30,00 USD E-book: 16,50 USD. Using the theory of holomorphic families of operators, we obtain a quantitative description of the absolutely continuous spectrum.

Publisher: American Mathematical Society. Journal description Manuscripts accepted for publication are similar in nature to those published in Transactions of the American. Further, they must be well-written and of interest to a substantial number of mathematicians.

They are particular instances of arithmetic groups. An arithmetic hyperbolic three-manifold is the quotient of hyperbolic space. by an arithmetic Kleinian group. These manifolds include some particularly beautiful or remarkable examples. A quaternion algebra over a field. is a four-dimensional central simple.

Epstein C L, The Spectral theory of geometrically periodic hyperbolic 3-manifolds,Mem. Pure Math (1980) (Providence, . American Mathematical Society)36 279–285Google Scholar. Soc. (1985) (Providence, . American Mathematical Society)58 Google Scholar. Froese R and Herbst I, Exponential bounds and absence of positive eigenvalues forN-body Schrödinger operators,Commun. Taylor M E,Pseudodifferential operators (1981) (Princeton, . Princeton University Press)Google Scholar.

Publisher: Amer Mathematical Society, 1998. In the spectral theory aspect of the work, they prove convergence of heat kernels. They then define a regularized heat trace associated to any finite volume, complete, hyperbolic three manifold, and study its asymptotic behavior through degeneration. As an application of the analysis of the regularized heat trace, they study asymptotic behavior of the spectral zeta function, determinant of the Laplacian, Selberg zeta function, and spectral counting functions through degeneration.