Author : Miki Hirano
Publisher : American Mathematical Society
Page : 136 pages
File Size : 20,45 MB
Release : 2022-07-18
Category : Mathematics
ISBN : 1470452774
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Author : Yoshinori Hamahata
Publisher : World Scientific
Page : 388 pages
File Size : 19,5 MB
Release : 2012
Category : Mathematics
ISBN : 9814355607
This volume contains contributions of principal speakers of the symposium on geometry and analysis of automorphic forms of several variables, held in September 2009 at Tokyo, Japan, in honor of Takayuki Oda''s 60th birthday. It presents both research and survey articles in the fields that are the main themes of his work. The volume may serve as a guide to developing areas as well as a resource for researchers who seek a broader view and for students who are beginning to explore automorphic form.
Author : Srikanth B. Iyengar
Publisher : American Mathematical Society
Page : 108 pages
File Size : 31,48 MB
Release : 2022-07-19
Category : Mathematics
ISBN : 1470471590
This book is aimed to provide an introduction to local cohomology which takes cognizance of the breadth of its interactions with other areas of mathematics. It covers topics such as the number of defining equations of algebraic sets, connectedness properties of algebraic sets, connections to sheaf cohomology and to de Rham cohomology, Gröbner bases in the commutative setting as well as for $D$-modules, the Frobenius morphism and characteristic $p$ methods, finiteness properties of local cohomology modules, semigroup rings and polyhedral geometry, and hypergeometric systems arising from semigroups. The book begins with basic notions in geometry, sheaf theory, and homological algebra leading to the definition and basic properties of local cohomology. Then it develops the theory in a number of different directions, and draws connections with topology, geometry, combinatorics, and algorithmic aspects of the subject.
Author : Ellen Elizabeth Eischen
Publisher : American Mathematical Society
Page : 199 pages
File Size : 47,83 MB
Release : 2024-03-26
Category : Mathematics
ISBN : 1470474921
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 : Wen-Wei Li
Publisher : Springer
Page : 148 pages
File Size : 33,76 MB
Release : 2018-11-02
Category : Mathematics
ISBN : 3030012883
This book focuses on a conjectural class of zeta integrals which arose from a program born in the work of Braverman and Kazhdan around the year 2000, the eventual goal being to prove the analytic continuation and functional equation of automorphic L-functions. Developing a general framework that could accommodate Schwartz spaces and the corresponding zeta integrals, the author establishes a formalism, states desiderata and conjectures, draws implications from these assumptions, and shows how known examples fit into this framework, supporting Sakellaridis' vision of the subject. The collected results, both old and new, and the included extensive bibliography, will be valuable to anyone who wishes to understand this program, and to those who are already working on it and want to overcome certain frequently occurring technical difficulties.
Author : H. Jacquet
Publisher : Springer
Page : 156 pages
File Size : 42,85 MB
Release : 2006-11-15
Category : Mathematics
ISBN : 3540376127
Author :
Publisher :
Page : 984 pages
File Size : 50,35 MB
Release : 2007
Category : Mathematics
ISBN :
Author : Stephen Gelbart
Publisher : Academic Press
Page : 142 pages
File Size : 19,7 MB
Release : 2014-07-14
Category : Mathematics
ISBN : 1483261034
Analytic Properties of Automorphic L-Functions is a three-chapter text that covers considerable research works on the automorphic L-functions attached by Langlands to reductive algebraic groups. Chapter I focuses on the analysis of Jacquet-Langlands methods and the Einstein series and Langlands’ so-called “Euler products . This chapter explains how local and global zeta-integrals are used to prove the analytic continuation and functional equations of the automorphic L-functions attached to GL(2). Chapter II deals with the developments and refinements of the zeta-inetgrals for GL(n). Chapter III describes the results for the L-functions L (s, ?, r), which are considered in the constant terms of Einstein series for some quasisplit reductive group. This book will be of value to undergraduate and graduate mathematics students.
Author : Ameya Pitale
Publisher : American Mathematical Soc.
Page : 120 pages
File Size : 17,74 MB
Release : 2014-09-29
Category : Mathematics
ISBN : 0821898566
Let be the automorphic representation of generated by a full level cuspidal Siegel eigenform that is not a Saito-Kurokawa lift, and be an arbitrary cuspidal, automorphic representation of . Using Furusawa's integral representation for combined with a pullback formula involving the unitary group , the authors prove that the -functions are "nice". The converse theorem of Cogdell and Piatetski-Shapiro then implies that such representations have a functorial lifting to a cuspidal representation of . Combined with the exterior-square lifting of Kim, this also leads to a functorial lifting of to a cuspidal representation of . As an application, the authors obtain analytic properties of various -functions related to full level Siegel cusp forms. They also obtain special value results for and
Author : Richard K. Guy
Publisher :
Page : 784 pages
File Size : 25,8 MB
Release : 1984
Category : Mathematical reviews
ISBN :
