Holomorphic Automorphic Forms and Cohomology
Author: Roelof Bruggeman
Publisher: American Mathematical Soc.
Published: 2018-05-29
Total Pages: 167
ISBN-13: 1470428555
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Cohomology of Arithmetic Groups and Automorphic Forms
Author: Jean-Pierre Labesse
Publisher: Springer
Published: 2006-11-14
Total Pages: 358
ISBN-13: 3540468765
DOWNLOAD EBOOK →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.
Modular And Automorphic Forms & Beyond
Author: Hossein Movasati
Publisher: World Scientific
Published: 2021-10-12
Total Pages: 323
ISBN-13: 9811238693
DOWNLOAD EBOOK →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'.
Representation Theory and Automorphic Forms
Author: Toshiyuki Kobayashi
Publisher: Springer Science & Business Media
Published: 2007-10-10
Total Pages: 220
ISBN-13: 0817646469
DOWNLOAD EBOOK →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.
Special Values of Automorphic Cohomology Classes
Author: Mark Green
Publisher: American Mathematical Soc.
Published: 2014-08-12
Total Pages: 158
ISBN-13: 0821898574
DOWNLOAD EBOOK →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.
Automorphic Forms and Related Geometry: Assessing the Legacy of I.I. Piatetski-Shapiro
Author: James W. Cogdell
Publisher: American Mathematical Soc.
Published: 2014-04-01
Total Pages: 454
ISBN-13: 0821893947
DOWNLOAD EBOOK →This volume contains the proceedings of the conference Automorphic Forms and Related Geometry: Assessing the Legacy of I.I. Piatetski-Shapiro, held from April 23-27, 2012, at Yale University, New Haven, CT. Ilya I. Piatetski-Shapiro, who passed away on 21 February 2009, was a leading figure in the theory of automorphic forms. The conference attempted both to summarize and consolidate the progress that was made during Piatetski-Shapiro's lifetime by him and a substantial group of his co-workers, and to promote future work by identifying fruitful directions of further investigation. It was organized around several themes that reflected Piatetski-Shapiro's main foci of work and that have promise for future development: functoriality and converse theorems; local and global -functions and their periods; -adic -functions and arithmetic geometry; complex geometry; and analytic number theory. In each area, there were talks to review the current state of affairs with special attention to Piatetski-Shapiro's contributions, and other talks to report on current work and to outline promising avenues for continued progress. The contents of this volume reflect most of the talks that were presented at the conference as well as a few additional contributions. They all represent various aspects of the legacy of Piatetski-Shapiro.
Automorphic Forms and the Picard Number of an Elliptic Surface
Author: Peter F. Stiller
Publisher: Springer Science & Business Media
Published: 2013-04-17
Total Pages: 201
ISBN-13: 3322907082
DOWNLOAD EBOOK →In studying an algebraic surface E, which we assume is non-singular and projective over the field of complex numbers t, it is natural to study the curves on this surface. In order to do this one introduces various equivalence relations on the group of divisors (cycles of codimension one). One such relation is algebraic equivalence and we denote by NS(E) the group of divisors modulo algebraic equivalence which is called the N~ron-Severi group of the surface E. This is known to be a finitely generated abelian group which can be regarded naturally as a subgroup of 2 H (E,Z). The rank of NS(E) will be denoted p and is known as the Picard number of E. 2 Every divisor determines a cohomology class in H(E,E) which is of I type (1,1), that is to say a class in H(E,9!) which can be viewed as a 2 subspace of H(E,E) via the Hodge decomposition. The Hodge Conjecture asserts in general that every rational cohomology class of type (p,p) is algebraic. In our case this is the Lefschetz Theorem on (I,l)-classes: Every cohomology class 2 2 is the class associated to some divisor. Here we are writing H (E,Z) for 2 its image under the natural mapping into H (E,t). Thus NS(E) modulo 2 torsion is Hl(E,n!) n H(E,Z) and th 1 b i f h -~ p measures e a ge ra c part 0 t e cohomology.
Mixed Automorphic Forms, Torus Bundles, and Jacobi Forms
Author: Min Ho Lee
Publisher: Springer Science & Business Media
Published: 2004-05-13
Total Pages: 262
ISBN-13: 9783540219224
DOWNLOAD EBOOK →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.
Automorphic Forms, Automorphic Representations, and Arithmetic
Author: Robert S. Doran
Publisher: American Mathematical Soc.
Published: 1999
Total Pages: 346
ISBN-13: 0821810510
DOWNLOAD EBOOK →Holomorphic Hilbert Modular Forms
Author: Paul B. Garrett
Publisher: Chapman and Hall/CRC
Published: 1989-09-01
Total Pages: 304
ISBN-13: 9780534103446
DOWNLOAD EBOOK →An introduction to a substantial part of the theory of holomorphic Hilbert modular forms, associated L-functions, and their arithmetic. As such, it is an introduction to the theory of automorphic forms in general, especially to the arithmetic of holomorphic forms. Annotation copyrighted by Book News, Inc., Portland, OR
