Automorphic Forms

Automorphic Forms
Author: Anton Deitmar
Publisher: Springer Science & Business Media
Total Pages: 255
Release: 2012-08-29
Genre: Mathematics
ISBN: 144714435X

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.

Eisenstein Series and Automorphic Representations

Eisenstein Series and Automorphic Representations
Author: Philipp Fleig
Publisher: Cambridge Studies in Advanced
Total Pages: 587
Release: 2018-07-05
Genre: Mathematics
ISBN: 1107189926

Detailed exposition of automorphic representations and their relation to string theory, for mathematicians and theoretical physicists.

Automorphic Forms and Representations

Automorphic Forms and Representations
Author: Daniel Bump
Publisher: Cambridge University Press
Total Pages: 592
Release: 1998-11-28
Genre: Mathematics
ISBN: 9780521658188

This book takes advanced graduate students from the foundations to topics on the research frontier.

Automorphic Forms and the Langlands Program

Automorphic Forms and the Langlands Program
Author: Lizhen Ji
Publisher: International Press of Boston
Total Pages: 0
Release: 2010
Genre: Algebraic number theory
ISBN: 9781571461414

Consists of expanded lecture notes from a 2007 international conference in Guangzhou, China, at which several leading experts in number theory presented introductions to, and surveys of, many aspects of automorphic forms and the Langlands program.

Families of Automorphic Forms and the Trace Formula

Families of Automorphic Forms and the Trace Formula
Author: Werner Müller
Publisher: Springer
Total Pages: 581
Release: 2016-09-20
Genre: Mathematics
ISBN: 3319414240

Featuring the work of twenty-three internationally-recognized experts, this volume explores the trace formula, spectra of locally symmetric spaces, p-adic families, and other recent techniques from harmonic analysis and representation theory. Each peer-reviewed submission in this volume, based on the Simons Foundation symposium on families of automorphic forms and the trace formula held in Puerto Rico in January-February 2014, is the product of intensive research collaboration by the participants over the course of the seven-day workshop. The goal of each session in the symposium was to bring together researchers with diverse specialties in order to identify key difficulties as well as fruitful approaches being explored in the field. The respective themes were counting cohomological forms, p-adic trace formulas, Hecke fields, slopes of modular forms, and orbital integrals.

Representation Theory and Automorphic Forms

Representation Theory and Automorphic Forms
Author: T. N. Bailey
Publisher: American Mathematical Soc.
Total Pages: 490
Release: 1997
Genre: Mathematics
ISBN: 0821806092

The lectures from a course in the representation theory of semi- simple groups, automorphic forms, and the relations between them. The purpose is to help analysts make systematic use of Lie groups in work on harmonic analysis, differential equations, and mathematical physics; and to provide number theorists with the representation-theoretic input to Wiles's proof of Fermat's Last Theorem. Begins with an introductory treatment of structure theory and ends with the current status of functionality. Annotation copyrighted by Book News, Inc., Portland, OR

Automorphic Forms, Representation Theory and Arithmetic

Automorphic Forms, Representation Theory and Arithmetic
Author: S. Gelbart
Publisher: Springer
Total Pages: 358
Release: 2013-12-01
Genre: Mathematics
ISBN: 3662007347

International Colloquium an Automorphic Forms, Representation Theory and Arithmetic. Published for the Tata Institute of Fundamental Research, Bombay

Automorphic Forms and Galois Representations: Volume 1

Automorphic Forms and Galois Representations: Volume 1
Author: Fred Diamond
Publisher: Cambridge University Press
Total Pages: 385
Release: 2014-10-16
Genre: Mathematics
ISBN: 1316062333

Automorphic forms and Galois representations have played a central role in the development of modern number theory, with the former coming to prominence via the celebrated Langlands program and Wiles' proof of Fermat's Last Theorem. This two-volume collection arose from the 94th LMS-EPSRC Durham Symposium on 'Automorphic Forms and Galois Representations' in July 2011, the aim of which was to explore recent developments in this area. The expository articles and research papers across the two volumes reflect recent interest in p-adic methods in number theory and representation theory, as well as recent progress on topics from anabelian geometry to p-adic Hodge theory and the Langlands program. The topics covered in volume one include the Shafarevich Conjecture, effective local Langlands correspondence, p-adic L-functions, the fundamental lemma, and other topics of contemporary interest.