The Selberg Trace Formula for PSL (2,R) PDF Download
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Author: Dennis A. Hejhal
Publisher: Springer
ISBN: 3540409149
Category : Mathematics
Languages : en
Pages : 815
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Book Description
Author: Dennis A. Hejhal
Publisher: Springer
ISBN: 3540409149
Category : Mathematics
Languages : en
Pages : 815
Get Book Here
Book Description
Author: Dennis A. Hejhal
Publisher: Springer
ISBN: 3540379797
Category : Mathematics
Languages : en
Pages : 523
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Book Description
Author: Dennis A. Hejhal
Publisher:
ISBN: 9783662195222
Category :
Languages : en
Pages : 528
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Book Description
Author: Dennis A. Hejhal
Publisher: Springer
ISBN:
Category : Mathematics
Languages : en
Pages : 742
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Book Description
Author: Armand Borel
Publisher: Cambridge University Press
ISBN: 1316582639
Category : Mathematics
Languages : en
Pages : 204
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Book Description
This book provides an introduction to some aspects of the analytic theory of automorphic forms on G=SL2(R) or the upper-half plane X, with respect to a discrete subgroup G of G of finite covolume. The point of view is inspired by the theory of infinite dimensional unitary representations of G; this is introduced in the last sections, making this connection explicit. The topics treated include the construction of fundamental domains, the notion of automorphic form on G\G and its relationship with the classical automorphic forms on X, Poincare series, constant terms, cusp forms, finite dimensionality of the space of automorphic forms of a given type, compactness of certain convolution operators, Eisenstein series, unitary representations of G, and the spectral decomposition of L2 (G\G). The main prerequisites are some results in functional analysis (reviewed, with references) and some familiarity with the elementary theory of Lie groups and Lie algebras. Graduate students and researchers in analytic number theory will find much to interest them in this book.
Author: Toyokazu Hiramatsu
Publisher: World Scientific
ISBN: 9813142286
Category : Mathematics
Languages : en
Pages : 188
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Book Description
This monograph provides a brief exposition of automorphic forms of weight 1 and their applications to arithmetic, especially to Galois representations. One of the outstanding problems in arithmetic is a generalization of class field theory to non-abelian Galois extension of number fields. In this volume, we discuss some relations between this problem and cusp forms of weight 1.
Author: Jay Jorgenson
Publisher: Springer
ISBN: 3540490418
Category : Mathematics
Languages : en
Pages : 156
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Book Description
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.
Author: Dennis A. Hejhal
Publisher:
ISBN:
Category : Automorphic forms
Languages : en
Pages : 516
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Book Description
Author: Andreas Juhl
Publisher: Birkhäuser
ISBN: 3034883404
Category : Mathematics
Languages : en
Pages : 712
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Book Description
Dynamical zeta functions are associated to dynamical systems with a countable set of periodic orbits. The dynamical zeta functions of the geodesic flow of lo cally symmetric spaces of rank one are known also as the generalized Selberg zeta functions. The present book is concerned with these zeta functions from a cohomological point of view. Originally, the Selberg zeta function appeared in the spectral theory of automorphic forms and were suggested by an analogy between Weil's explicit formula for the Riemann zeta function and Selberg's trace formula ([261]). The purpose of the cohomological theory is to understand the analytical properties of the zeta functions on the basis of suitable analogs of the Lefschetz fixed point formula in which periodic orbits of the geodesic flow take the place of fixed points. This approach is parallel to Weil's idea to analyze the zeta functions of pro jective algebraic varieties over finite fields on the basis of suitable versions of the Lefschetz fixed point formula. The Lefschetz formula formalism shows that the divisors of the rational Hassc-Wcil zeta functions are determined by the spectra of Frobenius operators on l-adic cohomology.
Author: Dennis A. Hejhal
Publisher: Springer Science & Business Media
ISBN: 1461215447
Category : Mathematics
Languages : en
Pages : 693
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Book Description
Most people tend to view number theory as the very paradigm of pure mathematics. With the advent of computers, however, number theory has been finding an increasing number of applications in practical settings, such as in cryptography, random number generation, coding theory, and even concert hall acoustics. Yet other applications are still emerging - providing number theorists with some major new areas of opportunity. The 1996 IMA summer program on Emerging Applications of Number Theory was aimed at stimulating further work with some of these newest (and most attractive) applications. Concentration was on number theory's recent links with: (a) wave phenomena in quantum mechanics (more specifically, quantum chaos); and (b) graph theory (especially expander graphs and related spectral theory). This volume contains the contributed papers from that meeting and will be of interest to anyone intrigued by novel applications of modern number-theoretical techniques.
