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:
ISBN:
Category : Automorphic forms
Languages : en
Pages : 544
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Book Description
Author: Dennis A. Hejhal
Publisher: Springer
ISBN: 3540379797
Category : Mathematics
Languages : en
Pages : 523
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Book Description
Author: Markus Szymon Fraczek
Publisher: Springer
ISBN: 331951296X
Category : Mathematics
Languages : en
Pages : 363
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Book Description
This book presents a method for evaluating Selberg zeta functions via transfer operators for the full modular group and its congruence subgroups with characters. Studying zeros of Selberg zeta functions for character deformations allows us to access the discrete spectra and resonances of hyperbolic Laplacians under both singular and non-singular perturbations. Areas in which the theory has not yet been sufficiently developed, such as the spectral theory of transfer operators or the singular perturbation theory of hyperbolic Laplacians, will profit from the numerical experiments discussed in this book. Detailed descriptions of numerical approaches to the spectra and eigenfunctions of transfer operators and to computations of Selberg zeta functions will be of value to researchers active in analysis, while those researchers focusing more on numerical aspects will benefit from discussions of the analytic theory, in particular those concerning the transfer operator method and the spectral theory of hyperbolic spaces.
Author: Jean-Michel Combes
Publisher: American Mathematical Soc.
ISBN: 0821842412
Category : Mathematics
Languages : en
Pages : 266
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Book Description
This volume consists of refereed research articles written by some of the speakers at this international conference in honor of the sixty-fifth birthday of Jean-Michel Combes. The topics span modern mathematical physics with contributions on state-of-the-art results in the theory of random operators, including localization for random Schrodinger operators with general probability measures, random magnetic Schrodinger operators, and interacting multiparticle operators with random potentials; transport properties of Schrodinger operators and classical Hamiltonian systems; equilibrium and nonequilibrium properties of open quantum systems; semiclassical methods for multiparticle systems and long-time evolution of wave packets; modeling of nanostructures; properties of eigenfunctions for first-order systems and solutions to the Ginzburg-Landau system; effective Hamiltonians for quantum resonances; quantum graphs, including scattering theory and trace formulas; random matrix theory; and quantum information theory. Graduate students and researchers will benefit from the accessibility of these articles and their current bibliographies.
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.
Author: William Duke
Publisher: American Mathematical Soc.
ISBN: 9780821843079
Category : Mathematics
Languages : en
Pages : 270
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Book Description
Articles in this volume are based on talks given at the Gauss-Dirichlet Conference held in Gottingen on June 20-24, 2005. The conference commemorated the 150th anniversary of the death of C.-F. Gauss and the 200th anniversary of the birth of J.-L. Dirichlet. The volume begins with a definitive summary of the life and work of Dirichlet and continues with thirteen papers by leading experts on research topics of current interest in number theory that were directly influenced by Gauss and Dirichlet. Among the topics are the distribution of primes (long arithmetic progressions of primes and small gaps between primes), class groups of binary quadratic forms, various aspects of the theory of $L$-functions, the theory of modular forms, and the study of rational and integral solutions to polynomial equations in several variables. Information for our distributors: Titles in this series are co-published with the Clay Mathematics Institute (Cambridge, MA).
Author: Nicolas Bergeron
Publisher: Springer
ISBN: 3319276662
Category : Mathematics
Languages : en
Pages : 375
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Book Description
This text is an introduction to the spectral theory of the Laplacian on compact or finite area hyperbolic surfaces. For some of these surfaces, called “arithmetic hyperbolic surfaces”, the eigenfunctions are of arithmetic nature, and one may use analytic tools as well as powerful methods in number theory to study them. After an introduction to the hyperbolic geometry of surfaces, with a special emphasis on those of arithmetic type, and then an introduction to spectral analytic methods on the Laplace operator on these surfaces, the author develops the analogy between geometry (closed geodesics) and arithmetic (prime numbers) in proving the Selberg trace formula. Along with important number theoretic applications, the author exhibits applications of these tools to the spectral statistics of the Laplacian and the quantum unique ergodicity property. The latter refers to the arithmetic quantum unique ergodicity theorem, recently proved by Elon Lindenstrauss. The fruit of several graduate level courses at Orsay and Jussieu, The Spectrum of Hyperbolic Surfaces allows the reader to review an array of classical results and then to be led towards very active areas in modern mathematics.
Author: Katsumi Nomizu
Publisher: American Mathematical Soc.
ISBN: 9780821875117
Category : Geometry, Algebraic
Languages : en
Pages : 170
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Book Description
This book presents papers that originally appeared in the Japanese journal Sugaku. The papers explore the relationship between number theory, algebraic geometry, and differential geometry.
Author: Jens Bölte
Publisher: Cambridge University Press
ISBN: 1107610494
Category : Mathematics
Languages : en
Pages : 285
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Book Description
Leading experts introduce this classical subject with exciting new applications in theoretical physics.
