Spectral Methods of Automorphic Forms
Title | Spectral Methods of Automorphic Forms PDF eBook |
Author | Henryk Iwaniec |
Publisher | American Mathematical Society, Revista Matemática Iberoamericana (RMI), Madrid, Spain |
Pages | 220 |
Release | 2021-11-17 |
Genre | Mathematics |
ISBN | 1470466228 |
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
Title | Introduction to the Spectral Theory of Automorphic Forms PDF eBook |
Author | Henryk Iwaniec |
Publisher | |
Pages | 272 |
Release | 1995 |
Genre | Automorphic forms |
ISBN |
Studies in the Analytic and Spectral Theory of Automorphic Forms
Title | Studies in the Analytic and Spectral Theory of Automorphic Forms PDF eBook |
Author | Andreas Strömbergsson |
Publisher | |
Pages | 226 |
Release | 2001 |
Genre | Differential operators |
ISBN | 9789150614565 |
Some Applications of the Spectral Theory of Automorphic Forms
Title | Some Applications of the Spectral Theory of Automorphic Forms PDF eBook |
Author | |
Publisher | |
Pages | 96 |
Release | 2011 |
Genre | |
ISBN |
Spectral Theory of Automorphic Functions
Title | Spectral Theory of Automorphic Functions PDF eBook |
Author | A. B. Venkov |
Publisher | American Mathematical Soc. |
Pages | 196 |
Release | 1983 |
Genre | Mathematics |
ISBN | 9780821830789 |
Families of Automorphic Forms
Title | Families of Automorphic Forms PDF eBook |
Author | Roelof W. Bruggeman |
Publisher | Springer Science & Business Media |
Pages | 320 |
Release | 2010-02-28 |
Genre | Mathematics |
ISBN | 3034603363 |
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 Methods
Title | Spectral Methods PDF eBook |
Author | Claudio Canuto |
Publisher | Springer Science & Business Media |
Pages | 585 |
Release | 2007-09-23 |
Genre | Science |
ISBN | 3540307265 |
Since the publication of "Spectral Methods in Fluid Dynamics" 1988, spectral methods have become firmly established as a mainstream tool for scientific and engineering computation. The authors of that book have incorporated into this new edition the many improvements in the algorithms and the theory of spectral methods that have been made since then. This latest book retains the tight integration between the theoretical and practical aspects of spectral methods, and the chapters are enhanced with material on the Galerkin with numerical integration version of spectral methods. The discussion of direct and iterative solution methods is also greatly expanded.