Spectral Theory Of Automorphic Functions
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Spectral Theory Of Automorphic Functions
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Author : A. B. Venkov
language : en
Publisher: American Mathematical Soc.
Release Date : 1983
Spectral Theory Of Automorphic Functions written by A. B. Venkov and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1983 with Mathematics categories.
Spectral Theory Of Automorphic Functions
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Author : A B Venkov
language : en
Publisher:
Release Date : 1990-10-31
Spectral Theory Of Automorphic Functions written by A B Venkov and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990-10-31 with categories.
Spectral Methods Of Automorphic Forms
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Author : Henryk Iwaniec
language : en
Publisher: American Mathematical Society, Revista Matemática Iberoamericana (RMI), Madrid, Spain
Release Date : 2021-11-17
Spectral Methods Of Automorphic Forms written by Henryk Iwaniec and has been published by American Mathematical Society, Revista Matemática Iberoamericana (RMI), Madrid, Spain this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-11-17 with Mathematics categories.
Automorphic forms are one of the central topics of analytic number theory. In fact, they sit at the confluence of analysis, algebra, geometry, and number theory. In this book, Henryk Iwaniec once again displays his penetrating insight, powerful analytic techniques, and lucid writing style. The first edition of this book was an underground classic, both as a textbook and as a respected source for results, ideas, and references. Iwaniec treats the spectral theory of automorphic forms as the study of the space of $L^2$ functions on the upper half plane modulo a discrete subgroup. Key topics include Eisenstein series, estimates of Fourier coefficients, Kloosterman sums, the Selberg trace formula and the theory of small eigenvalues. Henryk Iwaniec was awarded the 2002 Cole Prize for his fundamental contributions to number theory.
Introduction To The Spectral Theory Of Automorphic Forms
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Author : Henryk Iwaniec
language : en
Publisher:
Release Date : 1995
Introduction To The Spectral Theory Of Automorphic Forms written by Henryk Iwaniec and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Automorphic forms categories.
Scattering Theory For Automorphic Functions
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Author : Peter D. Lax
language : en
Publisher: Princeton University Press
Release Date : 1976
Scattering Theory For Automorphic Functions written by Peter D. Lax and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1976 with Mathematics categories.
The application by Fadeev and Pavlov of the Lax-Phillips scattering theory to the automorphic wave equation led Professors Lax and Phillips to reexamine this development within the framework of their theory. This volume sets forth the results of that work in the form of new or more straightforward treatments of the spectral theory of the Laplace-Beltrami operator over fundamental domains of finite area; the meromorphic character over the whole complex plane of the Eisenstein series; and the Selberg trace formula. CONTENTS: 1. Introduction. 2. An abstract scattering theory. 3. A modified theory for second order equations with an indefinite energy form. 4. The Laplace-Beltrami operator for the modular group. 5. The automorphic wave equation. 6. Incoming and outgoing subspaces for the automorphic wave equations. 7. The scattering matrix for the automorphic wave equation. 8. The general case. 9. The Selberg trace formula.
Families Of Automorphic Forms
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Author : Roelof W. Bruggeman
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-02-28
Families Of Automorphic Forms written by Roelof W. Bruggeman and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-02-28 with Mathematics categories.
Automorphic forms on the upper half plane have been studied for a long time. Most attention has gone to the holomorphic automorphic forms, with numerous applications to number theory. Maass, [34], started a systematic study of real analytic automorphic forms. He extended Hecke’s relation between automorphic forms and Dirichlet series to real analytic automorphic forms. The names Selberg and Roelcke are connected to the spectral theory of real analytic automorphic forms, see, e. g. , [50], [51]. This culminates in the trace formula of Selberg, see, e. g. , Hejhal, [21]. Automorphicformsarefunctionsontheupperhalfplanewithaspecialtra- formation behavior under a discontinuous group of non-euclidean motions in the upper half plane. One may ask how automorphic forms change if one perturbs this group of motions. This question is discussed by, e. g. , Hejhal, [22], and Phillips and Sarnak, [46]. Hejhal also discusses the e?ect of variation of the multiplier s- tem (a function on the discontinuous group that occurs in the description of the transformation behavior of automorphic forms). In [5]–[7] I considered variation of automorphic forms for the full modular group under perturbation of the m- tiplier system. A method based on ideas of Colin de Verdi` ere, [11], [12], gave the meromorphic continuation of Eisenstein and Poincar ́ e series as functions of the eigenvalue and the multiplier system jointly. The present study arose from a plan to extend these results to much more general groups (discrete co?nite subgroups of SL (R)).
Spectral Theory Of The Riemann Zeta Function
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Author : Yoichi Motohashi
language : en
Publisher: Cambridge University Press
Release Date : 1997-09-11
Spectral Theory Of The Riemann Zeta Function written by Yoichi Motohashi and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-09-11 with Mathematics categories.
The Riemann zeta function is one of the most studied objects in mathematics, and is of fundamental importance. In this book, based on his own research, Professor Motohashi shows that the function is closely bound with automorphic forms and that many results from there can be woven with techniques and ideas from analytic number theory to yield new insights into, and views of, the zeta function itself. The story starts with an elementary but unabridged treatment of the spectral resolution of the non-Euclidean Laplacian and the trace formulas. This is achieved by the use of standard tools from analysis rather than any heavy machinery, forging a substantial aid for beginners in spectral theory as well. These ideas are then utilized to unveil an image of the zeta-function, first perceived by the author, revealing it to be the main gem of a necklace composed of all automorphic L-functions. In this book, readers will find a detailed account of one of the most fascinating stories in the development of number theory, namely the fusion of two main fields in mathematics that were previously studied separately.
Spectral Theory For Bounded Functions And Applications To Evolution Equations
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Author : Gaston M. N'Guerekata
language : en
Publisher: Nova Science Publishers
Release Date : 2017
Spectral Theory For Bounded Functions And Applications To Evolution Equations written by Gaston M. N'Guerekata and has been published by Nova Science Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017 with MATHEMATICS categories.
One of the central questions in the qualitative theory of difference and differential equations is to find the conditions of existence and asymptotic behavior of bounded solutions. For equations with almost periodic coefficients, the problem concerns Favard and Perron. A remarkable theory has been developed in harmonic analysis with outstanding contributions by Loomis, Arendt, Batty, Lyubic, Phong, Naito, Minh and many others, when the Carleman spectrum of the functions is countable. Uniform continuity in this case plays a key role. In the absence of this condition, the theory does not apply. This led to the introduction over the last decade of new types of spectrum functions which helped solve the problem, especially in the case of almost automorphic functions by using the theory of commutating operators.This monograph presents a unique and unified manner of recent developments in the theory of bounded continuous functions, including the space of (Bohr) almost periodic functions and some of their generalizations, and the spaces of (Bochner) almost automorphic functions and almost automorphic sequences. Classical concepts from harmonic analysis such as the Bohr spectrum, Beurling spectrum and Carleman spectrum are also presented with some examples. Special attention is devoted to the recently introduced concepts of uniform spectrum and circular spectrum of bounded functions derived from the study of linear differential equation solutions, whose forcing terms are not necessarily uniformly continuous. Connections between these various types of spectra are also investigated. The book provides a semigroup-free study of the existence and asymptotic behavior of mild solutions concerning evolution equations of the first and second order as well as difference equations. Bibliographical and historical notes complete the major chapters. An appendix reviewing basic results on the theory of commutating operators is given. The content is presented in a way that is easily accessible to readers who are working in differential equations, but are not familiar with harmonic analysis and advanced functional analysis. It's our hope that this first monograph ever on this topic will attract more researchers.
Spectral Decomposition And Eisenstein Series
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Author : Colette Moeglin
language : en
Publisher: Cambridge University Press
Release Date : 1995-11-02
Spectral Decomposition And Eisenstein Series written by Colette Moeglin and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-11-02 with Mathematics categories.
A self-contained introduction to automorphic forms, and Eisenstein series and pseudo-series, proving some of Langlands' work at the intersection of number theory and group theory.
Spectral Theory Of Functions And Operators Ii
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Author :
language : en
Publisher: American Mathematical Soc.
Release Date : 1980
Spectral Theory Of Functions And Operators Ii written by and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1980 with Analytic functions categories.