Holomorphic Automorphic Forms And Cohomology
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Author |
: Roelof Bruggeman |
Publisher |
: American Mathematical Soc. |
Total Pages |
: 182 |
Release |
: 2018-05-29 |
ISBN-10 |
: 9781470428556 |
ISBN-13 |
: 1470428555 |
Rating |
: 4/5 (56 Downloads) |
Synopsis Holomorphic Automorphic Forms and Cohomology by : Roelof Bruggeman
Author |
: Jean-Pierre Labesse |
Publisher |
: Springer |
Total Pages |
: 358 |
Release |
: 2006-11-14 |
ISBN-10 |
: 9783540468769 |
ISBN-13 |
: 3540468765 |
Rating |
: 4/5 (69 Downloads) |
Synopsis Cohomology of Arithmetic Groups and Automorphic Forms by : Jean-Pierre Labesse
Cohomology of arithmetic groups serves as a tool in studying possible relations between the theory of automorphic forms and the arithmetic of algebraic varieties resp. the geometry of locally symmetric spaces. These proceedings will serve as a guide to this still rapidly developing area of mathematics. Besides two survey articles, the contributions are original research papers.
Author |
: Robert S. Doran |
Publisher |
: American Mathematical Soc. |
Total Pages |
: 293 |
Release |
: 1999 |
ISBN-10 |
: 9780821810507 |
ISBN-13 |
: 0821810502 |
Rating |
: 4/5 (07 Downloads) |
Synopsis Automorphic Forms, Automorphic Representations, and Arithmetic by : Robert S. Doran
Author |
: Hossein Movasati |
Publisher |
: World Scientific |
Total Pages |
: 323 |
Release |
: 2021-10-12 |
ISBN-10 |
: 9789811238697 |
ISBN-13 |
: 9811238693 |
Rating |
: 4/5 (97 Downloads) |
Synopsis Modular And Automorphic Forms & Beyond by : Hossein Movasati
The guiding principle in this monograph is to develop a new theory of modular forms which encompasses most of the available theory of modular forms in the literature, such as those for congruence groups, Siegel and Hilbert modular forms, many types of automorphic forms on Hermitian symmetric domains, Calabi-Yau modular forms, with its examples such as Yukawa couplings and topological string partition functions, and even go beyond all these cases. Its main ingredient is the so-called 'Gauss-Manin connection in disguise'.
Author |
: Ellen Elizabeth Eischen |
Publisher |
: American Mathematical Society |
Total Pages |
: 199 |
Release |
: 2024-03-26 |
ISBN-10 |
: 9781470474928 |
ISBN-13 |
: 1470474921 |
Rating |
: 4/5 (28 Downloads) |
Synopsis Automorphic Forms Beyond $mathrm {GL}_2$ by : Ellen Elizabeth Eischen
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.
Author |
: Toshiyuki Kobayashi |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 220 |
Release |
: 2007-10-10 |
ISBN-10 |
: 9780817646462 |
ISBN-13 |
: 0817646469 |
Rating |
: 4/5 (62 Downloads) |
Synopsis Representation Theory and Automorphic Forms by : Toshiyuki Kobayashi
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 |
: Mark Green |
Publisher |
: American Mathematical Soc. |
Total Pages |
: 158 |
Release |
: 2014-08-12 |
ISBN-10 |
: 9780821898574 |
ISBN-13 |
: 0821898574 |
Rating |
: 4/5 (74 Downloads) |
Synopsis Special Values of Automorphic Cohomology Classes by : Mark Green
The authors study the complex geometry and coherent cohomology of nonclassical Mumford-Tate domains and their quotients by discrete groups. Their focus throughout is on the domains which occur as open -orbits in the flag varieties for and , regarded as classifying spaces for Hodge structures of weight three. In the context provided by these basic examples, the authors formulate and illustrate the general method by which correspondence spaces give rise to Penrose transforms between the cohomologies of distinct such orbits with coefficients in homogeneous line bundles.
Author |
: Haruzo Hida |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 397 |
Release |
: 2012-12-06 |
ISBN-10 |
: 9781468493900 |
ISBN-13 |
: 1468493906 |
Rating |
: 4/5 (00 Downloads) |
Synopsis p-Adic Automorphic Forms on Shimura Varieties by : Haruzo Hida
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.
Author |
: Jean-Pierre Labesse |
Publisher |
: |
Total Pages |
: 368 |
Release |
: 2014-09-01 |
ISBN-10 |
: 3662204886 |
ISBN-13 |
: 9783662204887 |
Rating |
: 4/5 (86 Downloads) |
Synopsis Cohomology of Arithmetic Groups and Automorphic Forms by : Jean-Pierre Labesse
Author |
: Min Ho Lee |
Publisher |
: Springer |
Total Pages |
: 244 |
Release |
: 2004-04-30 |
ISBN-10 |
: 9783540409786 |
ISBN-13 |
: 3540409785 |
Rating |
: 4/5 (86 Downloads) |
Synopsis Mixed Automorphic Forms, Torus Bundles, and Jacobi Forms by : Min Ho Lee
This volume deals with various topics around equivariant holomorphic maps of Hermitian symmetric domains and is intended for specialists in number theory and algebraic geometry. In particular, it contains a comprehensive exposition of mixed automorphic forms that has never yet appeared in book form. The main goal is to explore connections among complex torus bundles, mixed automorphic forms, and Jacobi forms associated to an equivariant holomorphic map. Both number-theoretic and algebro-geometric aspects of such connections and related topics are discussed.