Eisenstein Series and Automorphic Representations PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Eisenstein Series and Automorphic Representations PDF full book. Access full book title Eisenstein Series and Automorphic Representations by Philipp Fleig. Download full books in PDF and EPUB format.
Author: Philipp Fleig
Publisher: Cambridge Studies in Advanced
ISBN: 1107189926
Category : Mathematics
Languages : en
Pages : 587
Get Book Here
Book Description
Detailed exposition of automorphic representations and their relation to string theory, for mathematicians and theoretical physicists.
Author: Philipp Fleig
Publisher: Cambridge Studies in Advanced
ISBN: 1107189926
Category : Mathematics
Languages : en
Pages : 587
Get Book Here
Book Description
Detailed exposition of automorphic representations and their relation to string theory, for mathematicians and theoretical physicists.
Author: Freydoon Shahidi
Publisher: American Mathematical Soc.
ISBN: 0821849891
Category : Mathematics
Languages : en
Pages : 218
Get Book Here
Book Description
This book presents a treatment of the theory of $L$-functions developed by means of the theory of Eisenstein series and their Fourier coefficients, a theory which is usually referred to as the Langlands-Shahidi method. The information gathered from this method, when combined with the converse theorems of Cogdell and Piatetski-Shapiro, has been quite sufficient in establishing a number of new cases of Langlands functoriality conjecture; at present, some of these cases cannot be obtained by any other method. These results have led to far-reaching new estimates for Hecke eigenvalues of Maass forms, as well as definitive solutions to certain problems in analytic and algebraic number theory. This book gives a detailed treatment of important parts of this theory, including a rather complete proof of Casselman-Shalika's formula for unramified Whittaker functions as well as a general treatment of the theory of intertwining operators. It also covers in some detail the global aspects of the method as well as some of its applications to group representations and harmonic analysis. This book is addressed to graduate students and researchers who are interested in the Langlands program in automorphic forms and its connections with number theory.
Author: Colette Moeglin
Publisher: Cambridge University Press
ISBN: 9780521418935
Category : Mathematics
Languages : en
Pages : 382
Get Book Here
Book Description
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.
Author: Philipp Fleig
Publisher: Cambridge University Press
ISBN: 1108118992
Category : Mathematics
Languages : en
Pages : 588
Get Book Here
Book Description
This introduction to automorphic forms on adelic groups G(A) emphasises the role of representation theory. The exposition is driven by examples, and collects and extends many results scattered throughout the literature, in particular the Langlands constant term formula for Eisenstein series on G(A) as well as the Casselman–Shalika formula for the p-adic spherical Whittaker function. This book also covers more advanced topics such as spherical Hecke algebras and automorphic L-functions. Many of these mathematical results have natural interpretations in string theory, and so some basic concepts of string theory are introduced with an emphasis on connections with automorphic forms. Throughout the book special attention is paid to small automorphic representations, which are of particular importance in string theory but are also of independent mathematical interest. Numerous open questions and conjectures, partially motivated by physics, are included to prompt the reader's own research.
Author: D. Bump
Publisher: Springer
ISBN: 3540390553
Category : Mathematics
Languages : en
Pages : 196
Get Book Here
Book Description
Author: Paul Garrett
Publisher: Cambridge University Press
ISBN: 1107154006
Category : Mathematics
Languages : en
Pages : 407
Get Book Here
Book Description
Volume 1 of a two-volume introduction to the analytical aspects of automorphic forms, featuring proofs of critical results with examples.
Author: S. Gelbart
Publisher: Springer
ISBN: 9783540106975
Category : Mathematics
Languages : en
Pages : 355
Get Book Here
Book Description
International Colloquium an Automorphic Forms, Representation Theory and Arithmetic. Published for the Tata Institute of Fundamental Research, Bombay
Author: Henryk Iwaniec
Publisher: American Mathematical Society, Revista Matemática Iberoamericana (RMI), Madrid, Spain
ISBN: 1470466228
Category : Mathematics
Languages : en
Pages : 220
Get Book Here
Book Description
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.
Author: H. Jacquet
Publisher: Springer
ISBN: 3540376127
Category : Mathematics
Languages : en
Pages : 156
Get Book Here
Book Description
Author: David Ginzburg
Publisher: World Scientific
ISBN: 9814304999
Category : Mathematics
Languages : en
Pages : 350
Get Book Here
Book Description
1. Introduction. 1.1. Overview. 1.2. Formulas for the Weil representation. 1.3. The case, where H is unitary and the place v splits in E -- 2. On certain residual representations. 2.1. The groups. 2.2. The Eisenstein series to be considered. 2.3. L-groups and representations related to P[symbol]. 2.4. The residue representation. 2.5. The case of a maximal parabolic subgroup (r = 1). 2.6. A preliminary lemma on Eisenstein series on GL[symbol]. 2.7. Constant terms of E(h, f[symbol]). 2.8. Description of W(M[symbol], D[symbol]). 2.9. Continuation of the proff of Theorem 2.1 -- 3. Coefficients of Gelfand-Graev type, of Fourier-Jacobi type, and descent. 3.1. Gelfand-Graev coefficients. 3.2. Fourier-Jacobi coefficients. 3.3. Nilpotent orbits. 3.4. Global integrals representing L-functions I. 3.5. Global integrals representing L-functions II. 3.6. Definition of the descent. 3.7. Definition of Jacquet modules corresponding to Gelfand-Graev characters. 3.8. Definition of Jacquet modules corresponding to Fourier-Jacobi characters -- 4. Some double coset decompositions. 4.1. The space Q[symbol]. 4.2. A set of representatives for Q[symbol]. 4.3. Stabilizers. 4.4. The set Q\h[symbol] -- 5. Jacquet modules of parabolic inductions : Gelfand-Graev characters. 5.1. The case where K is a field. 5.2. The case K = k[symbol]k -- 6. Jacquet modules of parabolic inductions : Fourier-Jacobi characters. 6.1. The case where K is a field. 6.2. The case K = k[symbol]k -- 7. The tower property. 7.1. A general lemma on "exchanging roots". 7.2. A formula for constant terms of Gelfand-Graev coefficients. 7.3. Global Gelfand-Graev models for cuspidal representations. 7.4. The general case : H is neither split nor quasi-split. 7.5. Global Gelfand-Graev models for the residual representations E[symbol]. 7.6. A formula for constant terms of Fourier-Jacobi coefficients. 7.7. Global Fourier-Jacobi models for cuspidal representations. 7.8. Global Fourier-Jacobi models for the residual representations E[symbol]
