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Author: Colette Moeglin
Publisher: Cambridge University Press
ISBN: 9780521418935
Category : Mathematics
Languages : en
Pages : 382
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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: Colette Moeglin
Publisher: Cambridge University Press
ISBN: 9780521418935
Category : Mathematics
Languages : en
Pages : 382
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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: Robert P. Langlands
Publisher: Springer
ISBN: 3540380701
Category : Mathematics
Languages : en
Pages : 344
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Book Description
Author: Henryk Iwaniec
Publisher: American Mathematical Society, Revista Matemática Iberoamericana (RMI), Madrid, Spain
ISBN: 1470466228
Category : Mathematics
Languages : en
Pages : 220
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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: Freydoon Shahidi
Publisher: American Mathematical Soc.
ISBN: 0821849891
Category : Mathematics
Languages : en
Pages : 218
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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: Philipp Fleig
Publisher: Cambridge Studies in Advanced
ISBN: 1107189926
Category : Mathematics
Languages : en
Pages : 587
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Book Description
Detailed exposition of automorphic representations and their relation to string theory, for mathematicians and theoretical physicists.
Author: Julia Mueller
Publisher: Cambridge University Press
ISBN: 1108710948
Category : Mathematics
Languages : en
Pages : 451
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Book Description
A step-by-step guide to Langlands' early work leading up the Langlands Program for mathematicians and advanced students.
Author: Shek-Tung Wong
Publisher: American Mathematical Soc.
ISBN: 0821824864
Category : Mathematics
Languages : en
Pages : 225
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Book Description
We carry out, in the context of an algebraic group and an arithmetic subgroup, an idea of Selberg for continuing Eisenstein series. It makes use of the theory of integral operators. The meromorphic continuation and functional equation of an Eisenstein series constructed with a cusp form on the Levi component of a rank one cuspidal subgroup are established.
Author: Paul Garrett
Publisher: Cambridge University Press
ISBN: 1107154006
Category : Mathematics
Languages : en
Pages : 407
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Book Description
Volume 1 of a two-volume introduction to the analytical aspects of automorphic forms, featuring proofs of critical results with examples.
Author: Armand Borel
Publisher: Cambridge University Press
ISBN: 9780521580496
Category : Mathematics
Languages : en
Pages : 226
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Book Description
An introduction to the analytic theory of automorphic forms in the case of fuchsian groups.
Author: Daniel Bump
Publisher: Cambridge University Press
ISBN: 9780521658188
Category : Mathematics
Languages : en
Pages : 592
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Book Description
This book takes advanced graduate students from the foundations to topics on the research frontier.
