Multiple Dirichlet Series L Functions And Automorphic Forms

Author : Daniel Bump
Publisher : Springer
ISBN 13 : 0817683348
Total Pages : 361 pages
Book Rating : 4.44/5 ( download)

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Download or read book Multiple Dirichlet Series, L-functions and Automorphic Forms written by Daniel Bump and published by Springer. This book was released on 2012-07-09 with total page 361 pages. Available in PDF, EPUB and Kindle. Book excerpt: Multiple Dirichlet Series, L-functions and Automorphic Forms gives the latest advances in the rapidly developing subject of Multiple Dirichlet Series, an area with origins in the theory of automorphic forms that exhibits surprising and deep connections to crystal graphs and mathematical physics. As such, it represents a new way in which areas including number theory, combinatorics, statistical mechanics, and quantum groups are seen to fit together. The volume also includes papers on automorphic forms and L-functions and related number-theoretic topics. This volume will be a valuable resource for graduate students and researchers in number theory, combinatorics, representation theory, mathematical physics, and special functions. Contributors: J. Beineke, B. Brubaker, D. Bump, G. Chinta, G. Cornelissen, C.A. Diaconu, S. Frechette, S. Friedberg, P. Garrett, D. Goldfeld, P.E. Gunnells, B. Heim, J. Hundley, D. Ivanov, Y. Komori, A.V. Kontorovich, O. Lorscheid, K. Matsumoto, P.J. McNamara, S.J. Patterson, M. Suzuki, H. Tsumura.

Author : Solomon Friedberg
Publisher : American Mathematical Soc.
ISBN 13 : 0821839632
Total Pages : 320 pages
Book Rating : 4.38/5 ( download)

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Download or read book Multiple Dirichlet Series, Automorphic Forms, and Analytic Number Theory written by Solomon Friedberg and published by American Mathematical Soc.. This book was released on 2006 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: Multiple Dirichlet series are Dirichlet series in several complex variables. A multiple Dirichlet series is said to be perfect if it satisfies a finite group of functional equations and has meromorphic continuation everywhere. The earliest examples came from Mellin transforms of metaplectic Eisenstein series and have been intensively studied over the last twenty years. More recently, many other examples have been discovered and it appears that all the classical theorems on moments of $L$-functions as well as the conjectures (such as those predicted by random matrix theory) can now be obtained via the theory of multiple Dirichlet series. Furthermore, new results, not obtainable by other methods, are just coming to light. This volume offers an account of some of the major research to date and the opportunities for the future. It includes an exposition of the main results in the theory of multiple Dirichlet series, and papers on moments of zeta- and $L$-functions, on new examples of multiple Dirichlet

Author : Ze-Li Dou
Publisher : Springer Science & Business Media
ISBN 13 : 3642287085
Total Pages : 131 pages
Book Rating : 4.84/5 ( download)

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Download or read book Six Short Chapters on Automorphic Forms and L-functions written by Ze-Li Dou and published by Springer Science & Business Media. This book was released on 2012-12-15 with total page 131 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Six Short Chapters on Automorphic Forms and L-functions" treats the period conjectures of Shimura and the moment conjecture. These conjectures are of central importance in contemporary number theory, but have hitherto remained little discussed in expository form. The book is divided into six short and relatively independent chapters, each with its own theme, and presents a motivated and lively account of the main topics, providing professionals an overall view of the conjectures and providing researchers intending to specialize in the area a guide to the relevant literature. Ze-Li Dou and Qiao Zhang are both associate professors of Mathematics at Texas Christian University, USA.

Author : Jan Hendrik Bruinier
Publisher : Springer
ISBN 13 : 3319697129
Total Pages : 366 pages
Book Rating : 4.23/5 ( download)

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Download or read book L-Functions and Automorphic Forms written by Jan Hendrik Bruinier and published by Springer. This book was released on 2018-02-22 with total page 366 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a collection of carefully refereed research articles and lecture notes stemming from the Conference "Automorphic Forms and L-Functions", held at the University of Heidelberg in 2016. The theory of automorphic forms and their associated L-functions is one of the central research areas in modern number theory, linking number theory, arithmetic geometry, representation theory, and complex analysis in many profound ways. The 19 papers cover a wide range of topics within the scope of the conference, including automorphic L-functions and their special values, p-adic modular forms, Eisenstein series, Borcherds products, automorphic periods, and many more.

Author : David Ginzburg
Publisher : American Mathematical Soc.
ISBN 13 : 0821847082
Total Pages : 339 pages
Book Rating : 4.84/5 ( download)

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Download or read book Automorphic Forms and $L$-functions II written by David Ginzburg and published by American Mathematical Soc.. This book was released on 2009 with total page 339 pages. Available in PDF, EPUB and Kindle. Book excerpt: Includes articles that represent global aspects of automorphic forms. This book covers topics such as: the trace formula; functoriality; representations of reductive groups over local fields; the relative trace formula and periods of automorphic forms; Rankin - Selberg convolutions and L-functions; and, p-adic L-functions.

Author : Freydoon Shahidi
Publisher : American Mathematical Soc.
ISBN 13 : 0821849891
Total Pages : 218 pages
Book Rating : 4.97/5 ( download)

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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 : Goro Shimura
Publisher : Springer Science & Business Media
ISBN 13 : 0387724745
Total Pages : 151 pages
Book Rating : 4.44/5 ( download)

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Download or read book Elementary Dirichlet Series and Modular Forms written by Goro Shimura and published by Springer Science & Business Media. This book was released on 2007-08-06 with total page 151 pages. Available in PDF, EPUB and Kindle. Book excerpt: A book on any mathematical subject beyond the textbook level is of little value unless it contains new ideas and new perspectives. It helps to include new results, provided that they give the reader new insights and are presented along with known old results in a clear exposition. It is with this philosophy that the author writes this volume. The two subjects, Dirichlet series and modular forms, are traditional subjects, but here they are treated in both orthodox and unorthodox ways. Regardless of the unorthodox treatment, the author has made the book accessible to those who are not familiar with such topics by including plenty of expository material.

Author : D. Bump
Publisher : Springer
ISBN 13 : 3540390553
Total Pages : 196 pages
Book Rating : 4.58/5 ( download)

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Download or read book Automorphic Forms on GL (3,TR) written by D. Bump and published by Springer. This book was released on 2006-12-08 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : H. Jacquet
Publisher : Springer
ISBN 13 : 3540376127
Total Pages : 156 pages
Book Rating : 4.25/5 ( download)

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Download or read book Automorphic Forms on GL (2) written by H. Jacquet and published by Springer. This book was released on 2006-11-15 with total page 156 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Dorian Goldfeld
Publisher : Cambridge University Press
ISBN 13 : 1139500139
Total Pages : 571 pages
Book Rating : 4.35/5 ( download)

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Download or read book Automorphic Representations and L-Functions for the General Linear Group: Volume 1 written by Dorian Goldfeld and published by Cambridge University Press. This book was released on 2011-04-21 with total page 571 pages. Available in PDF, EPUB and Kindle. Book excerpt: This graduate-level textbook provides an elementary exposition of the theory of automorphic representations and L-functions for the general linear group in an adelic setting. Definitions are kept to a minimum and repeated when reintroduced so that the book is accessible from any entry point, and with no prior knowledge of representation theory. The book includes concrete examples of global and local representations of GL(n), and presents their associated L-functions. In Volume 1, the theory is developed from first principles for GL(1), then carefully extended to GL(2) with complete detailed proofs of key theorems. Several proofs are presented for the first time, including Jacquet's simple and elegant proof of the tensor product theorem. In Volume 2, the higher rank situation of GL(n) is given a detailed treatment. Containing numerous exercises by Xander Faber, this book will motivate students and researchers to begin working in this fertile field of research.