Arithmeticity In The Theory Of Automorphic Forms
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Arithmeticity In The Theory Of Automorphic Forms
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Author : Goro Shimura
language : en
Publisher: American Mathematical Soc.
Release Date : 2000
Arithmeticity In The Theory Of Automorphic Forms written by Goro Shimura 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 2000 with Mathematics categories.
Written by one of the leading experts, venerable grandmasters, and most active contributors $\ldots$ in the arithmetic theory of automorphic forms $\ldots$ the new material included here is mainly the outcome of his extensive work $\ldots$ over the last eight years $\ldots$ a very careful, detailed introduction to the subject $\ldots$ this monograph is an important, comprehensively written and profound treatise on some recent achievements in the theory. --Zentralblatt MATH The main objects of study in this book are Eisenstein series and zeta functions associated with Hecke eigenforms on symplectic and unitary groups. After preliminaries--including a section, ``Notation and Terminology''--the first part of the book deals with automorphic forms on such groups. In particular, their rationality over a number field is defined and discussed in connection with the group action; also the reciprocity law for the values of automorphic functions at CM-points is proved. Next, certain differential operators that raise the weight are investigated in higher dimension. The notion of nearly holomorphic functions is introduced, and their arithmeticity is defined. As applications of these, the arithmeticity of the critical values of zeta functions and Eisenstein series is proved. Though the arithmeticity is given as the ultimate main result, the book discusses many basic problems that arise in number-theoretical investigations of automorphic forms but that cannot be found in expository forms. Examples of this include the space of automorphic forms spanned by cusp forms and certain Eisenstein series, transformation formulas of theta series, estimate of the Fourier coefficients of modular forms, and modular forms of half-integral weight. All these are treated in higher-dimensional cases. The volume concludes with an Appendix and an Index. The book will be of interest to graduate students and researchers in the field of zeta functions and modular forms.
Galois Theory And Modular Forms
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Author : Ki-ichiro Hashimoto
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-01
Galois Theory And Modular Forms written by Ki-ichiro Hashimoto 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 2013-12-01 with Mathematics categories.
This volume is an outgrowth of the research project "The Inverse Ga lois Problem and its Application to Number Theory" which was carried out in three academic years from 1999 to 2001 with the support of the Grant-in-Aid for Scientific Research (B) (1) No. 11440013. In September, 2001, an international conference "Galois Theory and Modular Forms" was held at Tokyo Metropolitan University after some preparatory work shops and symposia in previous years. The title of this book came from that of the conference, and the authors were participants of those meet All of the articles here were critically refereed by experts. Some of ings. these articles give well prepared surveys on branches of research areas, and many articles aim to bear the latest research results accompanied with carefully written expository introductions. When we started our re~earch project, we picked up three areas to investigate under the key word "Galois groups"; namely, "generic poly nomials" to be applied to number theory, "Galois coverings of algebraic curves" to study new type of representations of absolute Galois groups, and explicitly described "Shimura varieties" to understand well the Ga lois structures of some interesting polynomials including Brumer's sextic for the alternating group of degree 5. The topics of the articles in this volume are widely spread as a result. At a first glance, some readers may think this book somewhat unfocussed.
Harmonic Analysis Group Representations Automorphic Forms And Invariant Theory In Honor Of Roger E Howe
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Author : Jian-shu Li
language : en
Publisher: World Scientific
Release Date : 2007-11-12
Harmonic Analysis Group Representations Automorphic Forms And Invariant Theory In Honor Of Roger E Howe written by Jian-shu Li and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-11-12 with Mathematics categories.
This volume carries the same title as that of an international conference held at the National University of Singapore, 9-11 January 2006 on the occasion of Roger E. Howe's 60th birthday. Authored by leading members of the Lie theory community, these contributions, expanded from invited lectures given at the conference, are a fitting tribute to the originality, depth and influence of Howe's mathematical work. The range and diversity of the topics will appeal to a broad audience of research mathematicians and graduate students interested in symmetry and its profound applications.
Automorphic Forms And L Functions Ii
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Author : David Ginzburg
language : en
Publisher: American Mathematical Soc.
Release Date : 2009
Automorphic Forms And L Functions Ii written by David Ginzburg 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 2009 with Mathematics categories.
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.
Automorphic Forms Beyond Mathrm Gl 2
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Author : Ellen Elizabeth Eischen
language : en
Publisher: American Mathematical Society
Release Date : 2024-03-26
Automorphic Forms Beyond Mathrm Gl 2 written by Ellen Elizabeth Eischen and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-03-26 with Mathematics categories.
The Langlands program has been a very active and central field in mathematics ever since its conception over 50 years ago. It connects number theory, representation theory and arithmetic geometry, and other fields in a profound way. There are nevertheless very few expository accounts beyond the GL(2) case. This book features expository accounts of several topics on automorphic forms on higher rank groups, including rationality questions on unitary group, theta lifts and their applications to Arthur's conjectures, quaternionic modular forms, and automorphic forms over functions fields and their applications to inverse Galois problems. It is based on the lecture notes prepared for the twenty-fifth Arizona Winter School on “Automorphic Forms beyond GL(2)”, held March 5–9, 2022, at the University of Arizona in Tucson. The speakers were Ellen Eischen, Wee Teck Gan, Aaron Pollack, and Zhiwei Yun. The exposition of the book is in a style accessible to students entering the field. Advanced graduate students as well as researchers will find this a valuable introduction to various important and very active research areas.
Automorphic Representations L Functions And Applications Progress And Prospects
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Author : James W. Cogdell
language : en
Publisher: Walter de Gruyter
Release Date : 2011-06-24
Automorphic Representations L Functions And Applications Progress And Prospects written by James W. Cogdell and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-06-24 with Mathematics categories.
This volume is the proceedings of the conference on Automorphic Representations, L-functions and Applications: Progress and Prospects, held at the Department of Mathematics of The Ohio State University, March 27–30, 2003, in honor of the 60th birthday of Steve Rallis. The theory of automorphic representations, automorphic L-functions and their applications to arithmetic continues to be an area of vigorous and fruitful research. The contributed papers in this volume represent many of the most recent developments and directions, including Rankin–Selberg L-functions (Bump, Ginzburg–Jiang–Rallis, Lapid–Rallis) the relative trace formula (Jacquet, Mao–Rallis) automorphic representations (Gan–Gurevich, Ginzburg–Rallis–Soudry) representation theory of p-adic groups (Baruch, Kudla–Rallis, Mœglin, Cogdell–Piatetski-Shapiro–Shahidi) p-adic methods (Harris–Li–Skinner, Vigneras), and arithmetic applications (Chinta–Friedberg–Hoffstein). The survey articles by Bump, on the Rankin–Selberg method, and by Jacquet, on the relative trace formula, should be particularly useful as an introduction to the key ideas about these important topics. This volume should be of interest both to researchers and students in the area of automorphic representations, as well as to mathematicians in other areas interested in having an overview of current developments in this important field.
P Adic Automorphic Forms On Shimura Varieties
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Author : Haruzo Hida
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
P Adic Automorphic Forms On Shimura Varieties written by Haruzo Hida 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 2012-12-06 with Mathematics categories.
In the early years of the 1980s, while I was visiting the Institute for Ad vanced Study (lAS) at Princeton as a postdoctoral member, I got a fascinating view, studying congruence modulo a prime among elliptic modular forms, that an automorphic L-function of a given algebraic group G should have a canon ical p-adic counterpart of several variables. I immediately decided to find out the reason behind this phenomenon and to develop the theory of ordinary p-adic automorphic forms, allocating 10 to 15 years from that point, putting off the intended arithmetic study of Shimura varieties via L-functions and Eisenstein series (for which I visited lAS). Although it took more than 15 years, we now know (at least conjecturally) the exact number of variables for a given G, and it has been shown that this is a universal phenomenon valid for holomorphic automorphic forms on Shimura varieties and also for more general (nonholomorphic) cohomological automorphic forms on automorphic manifolds (in a markedly different way). When I was asked to give a series of lectures in the Automorphic Semester in the year 2000 at the Emile Borel Center (Centre Emile Borel) at the Poincare Institute in Paris, I chose to give an exposition of the theory of p-adic (ordinary) families of such automorphic forms p-adic analytically de pending on their weights, and this book is the outgrowth of the lectures given there.
Introduction To The Arithmetic Theory Of Automorphic Functions
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Author : Gorō Shimura
language : en
Publisher: Princeton University Press
Release Date : 1971-08-21
Introduction To The Arithmetic Theory Of Automorphic Functions written by Gorō Shimura and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1971-08-21 with Mathematics categories.
The theory of automorphic forms is playing increasingly important roles in several branches of mathematics, even in physics, and is almost ubiquitous in number theory. This book introduces the reader to the subject and in particular to elliptic modular forms with emphasis on their number-theoretical aspects. After two chapters geared toward elementary levels, there follows a detailed treatment of the theory of Hecke operators, which associate zeta functions to modular forms. At a more advanced level, complex multiplication of elliptic curves and abelian varieties is discussed. The main question is the construction of abelian extensions of certain algebraic number fields, which is traditionally called "Hilbert's twelfth problem." Another advanced topic is the determination of the zeta function of an algebraic curve uniformized by modular functions, which supplies an indispensable background for the recent proof of Fermat's last theorem by Wiles.
Hilbert Modular Forms And Iwasawa Theory
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Author : Haruzo Hida
language : en
Publisher: Clarendon Press
Release Date : 2006-06-15
Hilbert Modular Forms And Iwasawa Theory written by Haruzo Hida and has been published by Clarendon Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-06-15 with Mathematics categories.
The 1995 work of Wiles and Taylor-Wiles opened up a whole new technique in algebraic number theory and, a decade on, the waves caused by this incredibly important work are still being felt. This book, authored by a leading researcher, describes the striking applications that have been found for this technique. In the book, the deformation theoretic techniques of Wiles-Taylor are first generalized to Hilbert modular forms (following Fujiwara's treatment), and some applications found by the author are then discussed. With many exercises and open questions given, this text is ideal for researchers and graduate students entering this research area.
Arithmetic And Analytic Theories Of Quadratic Forms And Clifford Groups
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Author : Goro Shimura
language : en
Publisher: American Mathematical Soc.
Release Date : 2014-05-27
Arithmetic And Analytic Theories Of Quadratic Forms And Clifford Groups written by Goro Shimura 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 2014-05-27 with Education categories.
In this book, award-winning author Goro Shimura treats new areas and presents relevant expository material in a clear and readable style. Topics include Witt's theorem and the Hasse principle on quadratic forms, algebraic theory of Clifford algebras, spin groups, and spin representations. He also includes some basic results not readily found elsewhere. The two principle themes are: (1) Quadratic Diophantine equations; (2) Euler products and Eisenstein series on orthogonal groups and Clifford groups. The starting point of the first theme is the result of Gauss that the number of primitive representations of an integer as the sum of three squares is essentially the class number of primitive binary quadratic forms. Presented are a generalization of this fact for arbitrary quadratic forms over algebraic number fields and various applications. For the second theme, the author proves the existence of the meromorphic continuation of a Euler product associated with a Hecke eigenform on a Clifford or an orthogonal group. The same is done for an Eisenstein series on such a group. Beyond familiarity with algebraic number theory, the book is mostly self-contained. Several standard facts are stated with references for detailed proofs. Goro Shimura won the 1996 Steele Prize for Lifetime Achievement for "his important and extensive work on arithmetical geometry and automorphic forms".