Automorphic Forms
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Automorphic Forms On Gl 3 Tr
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Author : D. Bump
language : en
Publisher: Springer
Release Date : 2006-12-08
Automorphic Forms On Gl 3 Tr written by D. Bump and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-12-08 with Mathematics categories.
Automorphic Forms
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Author : Anton Deitmar
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-08-29
Automorphic Forms written by Anton Deitmar and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-08-29 with Mathematics categories.
Automorphic forms are an important complex analytic tool in number theory and modern arithmetic geometry. They played for example a vital role in Andrew Wiles's proof of Fermat's Last Theorem. This text provides a concise introduction to the world of automorphic forms using two approaches: the classic elementary theory and the modern point of view of adeles and representation theory. The reader will learn the important aims and results of the theory by focussing on its essential aspects and restricting it to the 'base field' of rational numbers. Students interested for example in arithmetic geometry or number theory will find that this book provides an optimal and easily accessible introduction into this topic.
Families Of Automorphic Forms
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Author : Roelof W. Bruggeman
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-02-28
Families Of Automorphic Forms written by Roelof W. Bruggeman and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-02-28 with Mathematics categories.
Automorphic forms on the upper half plane have been studied for a long time. Most attention has gone to the holomorphic automorphic forms, with numerous applications to number theory. Maass, [34], started a systematic study of real analytic automorphic forms. He extended Hecke’s relation between automorphic forms and Dirichlet series to real analytic automorphic forms. The names Selberg and Roelcke are connected to the spectral theory of real analytic automorphic forms, see, e. g. , [50], [51]. This culminates in the trace formula of Selberg, see, e. g. , Hejhal, [21]. Automorphicformsarefunctionsontheupperhalfplanewithaspecialtra- formation behavior under a discontinuous group of non-euclidean motions in the upper half plane. One may ask how automorphic forms change if one perturbs this group of motions. This question is discussed by, e. g. , Hejhal, [22], and Phillips and Sarnak, [46]. Hejhal also discusses the e?ect of variation of the multiplier s- tem (a function on the discontinuous group that occurs in the description of the transformation behavior of automorphic forms). In [5]–[7] I considered variation of automorphic forms for the full modular group under perturbation of the m- tiplier system. A method based on ideas of Colin de Verdi` ere, [11], [12], gave the meromorphic continuation of Eisenstein and Poincar ́ e series as functions of the eigenvalue and the multiplier system jointly. The present study arose from a plan to extend these results to much more general groups (discrete co?nite subgroups of SL (R)).
Automorphic Forms On Gl 2
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Author : H. Jacquet
language : en
Publisher: Springer
Release Date : 2006-11-15
Automorphic Forms On Gl 2 written by H. Jacquet and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.
Automorphic Forms And Applications
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Author : Peter Sarnak
language : en
Publisher: American Mathematical Soc.
Release Date : 2007
Automorphic Forms And Applications written by Peter Sarnak and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.
The theory of automorphic forms has seen dramatic developments in recent years. in particular, important instances of Langlands functoriality have been established. This volume presents three weeks of lectures from the IAS/Park City Mathematics Institute Summer School on automorphic forms and their applications. It addresses some of the general aspects of automorphic forms, as well as certain recent advances in the field. The book starts with the lectures of Borel on the basic theory of automorphic forms, which lay the foundation for the lectures by Cogdell and Shahidi on converse theorems and the Langlands-Shahidi method, as well as those by Clozel and Li on the Ramanujan conjectures and graphs. The analytic theory of GL(2)-forms and $L$-functions are the subject of Michel's lectures, while Terras covers arithmetic quantum chaos. The volume also includes a chapter by Vogan on isolated unitary representations, which is related to the lectures by Clozel. This volume is recommended for independent study or an advanced topics course. It is suitable for graduate students and researchers interested in automorphic forms and number theory. Information for our distributors: Titles in this series are co-published with the Institute for Advanced Study/Park City Mathematics Institute. Members of the Mathematical Association of America (MAA) and the National Council of Teachers of Mathematics (NCTM) receive a 20% discount from list price.
Automorphic Forms And Representations
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Author : Daniel Bump
language : en
Publisher: Cambridge University Press
Release Date : 1998-11-28
Automorphic Forms And Representations written by Daniel Bump and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-11-28 with Mathematics categories.
This book takes advanced graduate students from the foundations to topics on the research frontier.
Contributions To Automorphic Forms Geometry And Number Theory
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Author : Haruzo Hida
language : en
Publisher: JHU Press
Release Date : 2004-03-11
Contributions To Automorphic Forms Geometry And Number Theory written by Haruzo Hida and has been published by JHU Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-03-11 with Mathematics categories.
In Contributions to Automorphic Forms, Geometry, and Number Theory, Haruzo Hida, Dinakar Ramakrishnan, and Freydoon Shahidi bring together a distinguished group of experts to explore automorphic forms, principally via the associated L-functions, representation theory, and geometry. Because these themes are at the cutting edge of a central area of modern mathematics, and are related to the philosophical base of Wiles' proof of Fermat's last theorem, this book will be of interest to working mathematicians and students alike. Never previously published, the contributions to this volume expose the reader to a host of difficult and thought-provoking problems. Each of the extraordinary and noteworthy mathematicians in this volume makes a unique contribution to a field that is currently seeing explosive growth. New and powerful results are being proved, radically and continually changing the field's make up. Contributions to Automorphic Forms, Geometry, and Number Theory will likely lead to vital interaction among researchers and also help prepare students and other young mathematicians to enter this exciting area of pure mathematics. Contributors: Jeffrey Adams, Jeffrey D. Adler, James Arthur, Don Blasius, Siegfried Boecherer, Daniel Bump, William Casselmann, Laurent Clozel, James Cogdell, Laurence Corwin, Solomon Friedberg, Masaaki Furusawa, Benedict Gross, Thomas Hales, Joseph Harris, Michael Harris, Jeffrey Hoffstein, Hervé Jacquet, Dihua Jiang, Nicholas Katz, Henry Kim, Victor Kreiman, Stephen Kudla, Philip Kutzko, V. Lakshmibai, Robert Langlands, Erez Lapid, Ilya Piatetski-Shapiro, Dipendra Prasad, Stephen Rallis, Dinakar Ramakrishnan, Paul Sally, Freydoon Shahidi, Peter Sarnak, Rainer Schulze-Pillot, Joseph Shalika, David Soudry, Ramin Takloo-Bigash, Yuri Tschinkel, Emmanuel Ullmo, Marie-France Vignéras, Jean-Loup Waldspurger.
Automorphic Forms Automorphic Representations And Arithmetic
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Author : Robert S. Doran
language : en
Publisher: American Mathematical Soc.
Release Date : 1999
Automorphic Forms Automorphic Representations And Arithmetic written by Robert S. Doran and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with categories.
Spectral Methods Of Automorphic Forms
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Author : Henryk Iwaniec
language : en
Publisher: American Mathematical Society, Revista Matemática Iberoamericana (RMI), Madrid, Spain
Release Date : 2021-11-17
Spectral Methods Of Automorphic Forms written by Henryk Iwaniec and has been published by American Mathematical Society, Revista Matemática Iberoamericana (RMI), Madrid, Spain this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-11-17 with Mathematics categories.
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.
Automorphic Forms And Geometry Of Arithmetic Varieties
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Author : Ki-ichiro Hashimoto
language : en
Publisher:
Release Date : 1989
Automorphic Forms And Geometry Of Arithmetic Varieties written by Ki-ichiro Hashimoto and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989 with Automorphic forms categories.