On the Functional Equations Satisfied by Eisenstein Series PDF Download

Author: Robert P. Langlands
Publisher: Springer
ISBN: 3540380701
Category : Mathematics
Languages : en
Pages : 344

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Author: Nikolaos Mandouvalos
Publisher: American Mathematical Soc.
ISBN: 0821824635
Category : Mathematics
Languages : en
Pages : 97

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Book Description
In this memoir we have introduced and studied the scattering operator and the Eisenstein series and we have formulated and proved the inner product formula and the "Maass-Selberg" relations for Kleinian groups.

Author: Wee Teck Gan
Publisher: Springer Science & Business Media
ISBN: 0817646396
Category : Mathematics
Languages : en
Pages : 317

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Book Description
Eisenstein series are an essential ingredient in the spectral theory of automorphic forms and an important tool in the theory of L-functions. They have also been exploited extensively by number theorists for many arithmetic purposes. Bringing together contributions from areas which do not usually interact with each other, this volume introduces diverse users of Eisenstein series to a variety of important applications. With this juxtaposition of perspectives, the reader obtains deeper insights into the arithmetic of Eisenstein series. The central theme of the exposition focuses on the common structural properties of Eisenstein series occurring in many related applications.

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: 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 University Press
ISBN: 1108118992
Category : Mathematics
Languages : en
Pages : 588

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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: Gorō Shimura
Publisher: American Mathematical Soc.
ISBN: 0821805746
Category : Mathematics
Languages : en
Pages : 282

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Book Description
This volume has three chief objectives: 1) the determination of local Euler factors on classical groups in an explicit rational form; 2) Euler products and Eisenstein series on a unitary group of an arbitrary signature; and 3) a class number formula for a totally definite hermitian form. Though these are new results that have never before been published, Shimura starts with a quite general setting. He includes many topics of an expository nature so that the book can be viewed as an introduction to the theory of automorphic forms of several variables, Hecke theory in particular. Eventually, the exposition is specialized to unitary groups, but they are treated as a model case so that the reader can easily formulate the corresponding facts for other groups. There are various facts on algebraic groups and their localizations that are standard but were proved in some old papers or just called well-known. In this book, the reader will find the proofs of many of them, as well as systematic expositions of the topics. This is the first book in which the Hecke theory of a general (nonsplit) classical group is treated. The book is practically self-contained, except that familiarity with algebraic number theory is assumed.

Author: Bhartendu Harishchandra
Publisher: Springer
ISBN: 354035865X
Category : Mathematics
Languages : en
Pages : 152

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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: Jeffrey Adams
Publisher: American Mathematical Soc.
ISBN: 0821852469
Category : Mathematics
Languages : en
Pages : 404

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Book Description
This volume contains the proceedings of the conference on Representation Theory and Mathematical Physics, in honor of Gregg Zuckerman's 60th birthday, held October 24-27, 2009, at Yale University. Lie groups and their representations play a fundamental role in mathematics, in particular because of connections to geometry, topology, number theory, physics, combinatorics, and many other areas. Representation theory is one of the cornerstones of the Langlands program in number theory, dating to the 1970s. Zuckerman's work on derived functors, the translation principle, and coherent continuation lie at the heart of the modern theory of representations of Lie groups. One of the major unsolved problems in representation theory is that of the unitary dual. The fact that there is, in principle, a finite algorithm for computing the unitary dual relies heavily on Zuckerman's work. In recent years there has been a fruitful interplay between mathematics and physics, in geometric representation theory, string theory, and other areas. New developments on chiral algebras, representation theory of affine Kac-Moody algebras, and the geometric Langlands correspondence are some of the focal points of this volume. Recent developments in the geometric Langlands program point to exciting connections between certain automorphic representations and dual fibrations in geometric mirror symmetry.