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Author : Robert P. Langlands
Publisher : Springer
ISBN 13 : 3540380701
Total Pages : 344 pages
Book Rating : 4.5/5 (43 download)
Download or read book On the Functional Equations Satisfied by Eisenstein Series written by Robert P. Langlands and published by Springer. This book was released on 2006-11-14 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Nikolaos Mandouvalos
Publisher : American Mathematical Soc.
ISBN 13 : 0821824635
Total Pages : 97 pages
Book Rating : 4.8/5 (218 download)
Download or read book Scattering Operator, Eisenstein Series, Inner Product Formula and ``Maass-Selberg'' Relations for Kleinian Groups written by Nikolaos Mandouvalos and published by American Mathematical Soc.. This book was released on 1989 with total page 97 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 13 : 0817646396
Total Pages : 317 pages
Book Rating : 4.8/5 (176 download)
Download or read book Eisenstein Series and Applications written by Wee Teck Gan and published by Springer Science & Business Media. This book was released on 2007-12-22 with total page 317 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Freydoon Shahidi
Publisher : American Mathematical Soc.
ISBN 13 : 0821849891
Total Pages : 218 pages
Book Rating : 4.8/5 (218 download)
Download or read book Eisenstein Series and Automorphic $L$-Functions written by Freydoon Shahidi and published by American Mathematical Soc.. This book was released on 2010 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 13 : 1108118992
Total Pages : 588 pages
Book Rating : 4.1/5 (81 download)
Download or read book Eisenstein Series and Automorphic Representations written by Philipp Fleig and published by Cambridge University Press. This book was released on 2018-07-05 with total page 588 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 13 : 0821805746
Total Pages : 282 pages
Book Rating : 4.8/5 (218 download)
Download or read book Euler Products and Eisenstein Series written by Gorō Shimura and published by American Mathematical Soc.. This book was released on 1997 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 13 : 354035865X
Total Pages : 152 pages
Book Rating : 4.5/5 (43 download)
Download or read book Automorphic Forms on Semisimple Lie Groups written by Bhartendu Harishchandra and published by Springer. This book was released on 2006-12-08 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Julia Mueller
Publisher : Cambridge University Press
ISBN 13 : 1108710948
Total Pages : 451 pages
Book Rating : 4.1/5 (87 download)
Download or read book The Genesis of the Langlands Program written by Julia Mueller and published by Cambridge University Press. This book was released on 2021-08-05 with total page 451 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 13 : 0821852469
Total Pages : 404 pages
Book Rating : 4.8/5 (218 download)
Download or read book Representation Theory and Mathematical Physics written by Jeffrey Adams and published by American Mathematical Soc.. This book was released on 2011-11-07 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author : Ramesh Gangolli
Publisher : Springer Science & Business Media
ISBN 13 : 3642729568
Total Pages : 379 pages
Book Rating : 4.6/5 (427 download)
Download or read book Harmonic Analysis of Spherical Functions on Real Reductive Groups written by Ramesh Gangolli and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 379 pages. Available in PDF, EPUB and Kindle. Book excerpt: Analysis on Symmetric spaces, or more generally, on homogeneous spaces of semisimple Lie groups, is a subject that has undergone a vigorous development in recent years, and has become a central part of contemporary mathematics. This is only to be expected, since homogeneous spaces and group representations arise naturally in diverse contexts ranging from Number theory and Geometry to Particle Physics and Polymer Chemistry. Its explosive growth sometimes makes it difficult to realize that it is actually relatively young as mathematical theories go. The early ideas in the subject (as is the case with many others) go back to Elie Cart an and Hermann Weyl who studied the compact symmetric spaces in the 1930's. However its full development did not begin until the 1950's when Gel'fand and Harish Chandra dared to dream of a theory of representations that included all semisimple Lie groups. Harish-Chandra's theory of spherical functions was essentially complete in the late 1950's, and was to prove to be the forerunner of his monumental work on harmonic analysis on reductive groups that has inspired a whole generation of mathematicians. It is the harmonic analysis of spherical functions on symmetric spaces, that is at the focus of this book. The fundamental questions of harmonic analysis on symmetric spaces involve an interplay of the geometric, analytical, and algebraic aspects of these spaces. They have therefore attracted a great deal of attention, and there have been many excellent expositions of the themes that are characteristic of this subject.
Author : Alexei A. Panchishkin
Publisher : Springer
ISBN 13 : 3662215411
Total Pages : 167 pages
Book Rating : 4.6/5 (622 download)
Download or read book Non-Archimedean L-Functions written by Alexei A. Panchishkin and published by Springer. This book was released on 2013-11-11 with total page 167 pages. Available in PDF, EPUB and Kindle. Book excerpt: 1) p n=1 The set of arguments s for which ((s) is defined can be extended to all s E C,s :f:. 1, and we may regard C as the group of all continuous quasicharacters C = Hom(R~, c>
Author : Dorian Goldfeld
Publisher : Cambridge University Press
ISBN 13 : 1139456202
Total Pages : 65 pages
Book Rating : 4.1/5 (394 download)
Download or read book Automorphic Forms and L-Functions for the Group GL(n,R) written by Dorian Goldfeld and published by Cambridge University Press. This book was released on 2006-08-03 with total page 65 pages. Available in PDF, EPUB and Kindle. Book excerpt: L-functions associated to automorphic forms encode all classical number theoretic information. They are akin to elementary particles in physics. This book provides an entirely self-contained introduction to the theory of L-functions in a style accessible to graduate students with a basic knowledge of classical analysis, complex variable theory, and algebra. Also within the volume are many new results not yet found in the literature. The exposition provides complete detailed proofs of results in an easy-to-read format using many examples and without the need to know and remember many complex definitions. The main themes of the book are first worked out for GL(2,R) and GL(3,R), and then for the general case of GL(n,R). In an appendix to the book, a set of Mathematica functions is presented, designed to allow the reader to explore the theory from a computational point of view.
Author : Daniel Bump
Publisher : Cambridge University Press
ISBN 13 : 9780521658188
Total Pages : 592 pages
Book Rating : 4.6/5 (581 download)
Download or read book Automorphic Forms and Representations written by Daniel Bump and published by Cambridge University Press. This book was released on 1998-11-28 with total page 592 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book takes advanced graduate students from the foundations to topics on the research frontier.
Author : James Arthur
Publisher : American Mathematical Soc.
ISBN 13 : 0821852043
Total Pages : 658 pages
Book Rating : 4.8/5 (218 download)
Download or read book On Certain $L$-Functions written by James Arthur and published by American Mathematical Soc.. This book was released on 2011 with total page 658 pages. Available in PDF, EPUB and Kindle. Book excerpt: Illuminate various areas of the study of geometric, analytic, and number theoretic aspects of automorphic forms and their $L$-functions, and both local and global theory are addressed. Topics discussed in the articles include Langlands functoriality, the Rankin-Selberg method, the Langlands-Shahidi method, motivic Galois groups, Shimura varieties, orbital integrals, representations of $p$-adic groups, Plancherel formula and its consequences, and the Gross-Prasad conjecture.
Author : Toshiyuki Kobayashi
Publisher : Springer Science & Business Media
ISBN 13 : 0817646469
Total Pages : 220 pages
Book Rating : 4.8/5 (176 download)
Download or read book Representation Theory and Automorphic Forms written by Toshiyuki Kobayashi and published by Springer Science & Business Media. This book was released on 2007-10-10 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume uses a unified approach to representation theory and automorphic forms. It collects papers, written by leading mathematicians, that track recent progress in the expanding fields of representation theory and automorphic forms and their association with number theory and differential geometry. Topics include: Automorphic forms and distributions, modular forms, visible-actions, Dirac cohomology, holomorphic forms, harmonic analysis, self-dual representations, and Langlands Functoriality Conjecture, Both graduate students and researchers will find inspiration in this volume.
Author : A. Borel
Publisher : American Mathematical Soc.
ISBN 13 : 0821814354
Total Pages : 334 pages
Book Rating : 4.8/5 (218 download)
Download or read book Automorphic Forms, Representations and $L$-Functions written by A. Borel and published by American Mathematical Soc.. This book was released on 1979 with total page 334 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contains sections on Reductive groups, representations, Automorphic forms and representations.
Author : Colette Moeglin
Publisher : Cambridge University Press
ISBN 13 : 9780521418935
Total Pages : 382 pages
Book Rating : 4.4/5 (189 download)
Download or read book Spectral Decomposition and Eisenstein Series written by Colette Moeglin and published by Cambridge University Press. This book was released on 1995-11-02 with total page 382 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
