Automorphic Forms and L-Functions for the Group GL(n,R)

Author: Dorian Goldfeld

Publisher: Cambridge University Press

ISBN: 1139456202

Category: Mathematics

Page: N.A

View: 8002

L-functions associated to automorphic forms encode all classical number theoretic information. They are akin to elementary particles in physics. This 2006 book provides an entirely self-contained introduction to the theory of L-functions in a style accessible to graduate students with a basic knowledge of classical analysis, complex variable theory, and algebra. Also within the volume are many new results not yet found in the literature. The exposition provides complete detailed proofs of results in an easy-to-read format using many examples and without the need to know and remember many complex definitions. The main themes of the book are first worked out for GL(2,R) and GL(3,R), and then for the general case of GL(n,R). In an appendix to the book, a set of Mathematica functions is presented, designed to allow the reader to explore the theory from a computational point of view.
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Automorphic Representations and L-Functions for the General Linear Group:

Author: Dorian Goldfeld,Joseph Hundley

Publisher: Cambridge University Press

ISBN: 1139500139

Category: Mathematics

Page: N.A

View: 4537

This graduate-level textbook provides an elementary exposition of the theory of automorphic representations and L-functions for the general linear group in an adelic setting. Definitions are kept to a minimum and repeated when reintroduced so that the book is accessible from any entry point, and with no prior knowledge of representation theory. The book includes concrete examples of global and local representations of GL(n), and presents their associated L-functions. In Volume 1, the theory is developed from first principles for GL(1), then carefully extended to GL(2) with complete detailed proofs of key theorems. Several proofs are presented for the first time, including Jacquet's simple and elegant proof of the tensor product theorem. In Volume 2, the higher rank situation of GL(n) is given a detailed treatment. Containing numerous exercises by Xander Faber, this book will motivate students and researchers to begin working in this fertile field of research.
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Spectral Methods of Automorphic Forms

Author: Henryk Iwaniec

Publisher: American Mathematical Soc.

ISBN: 0821831607

Category: Mathematics

Page: 220

View: 1041

Automorphic forms are one of the central topics of analytic number theory. In fact, they sit at the confluence of analysis, algebra, geometry, and number theory. In this book, Henryk Iwaniec once again displays his penetrating insight, powerful analytic techniques, and lucid writing style. The first edition of this book was an underground classic, both as a textbook and as a respected source for results, ideas, and references. Iwaniec treats the spectral theory of automorphic forms as the study of the space of $L^2$ functions on the upper half plane modulo a discrete subgroup. Key topics include Eisenstein series, estimates of Fourier coefficients, Kloosterman sums, the Selberg trace formula and the theory of small eigenvalues. Henryk Iwaniec was awarded the 2002 Cole Prize for his fundamental contributions to number theory.
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Arithmetic of L-functions

Author: Cristian Popescu,Karl Rubin,Alice Silverberg

Publisher: American Mathematical Soc.

ISBN: 0821886983

Category: Mathematics

Page: 499

View: 1864

The overall theme of the 2009 IAS/PCMI Graduate Summer School was connections between special values of $L$-functions and arithmetic, especially the Birch and Swinnerton-Dyer Conjecture and Stark's Conjecture. These conjectures are introduced and discussed in depth, and progress made over the last 30 years is described. This volume contains the written versions of the graduate courses delivered at the summer school. It would be a suitable text for advanced graduate topics courses on the Birch and Swinnerton-Dyer Conjecture and/or Stark's Conjecture. The book will also serve as a reference volume for experts in the field.
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Families of Automorphic Forms and the Trace Formula

Author: Werner Müller,Sug Woo Shin,Nicolas Templier

Publisher: Springer

ISBN: 3319414240

Category: Mathematics

Page: 578

View: 9195

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.
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Automorphic Forms

Author: Anton Deitmar

Publisher: Springer Science & Business Media

ISBN: 144714435X

Category: Mathematics

Page: 252

View: 6128

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.
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Algebraic Homotopy

Author: Hans J. Baues

Publisher: Cambridge University Press

ISBN: 9780521333764

Category: Mathematics

Page: 466

View: 4596

This book gives a general outlook on homotopy theory; fundamental concepts, such as homotopy groups and spectral sequences, are developed from a few axioms and are thus available in a broad variety of contexts. Many examples and applications in topology and algebra are discussed, including an introduction to rational homotopy theory in terms of both differential Lie algebras and De Rham algebras. The author describes powerful tools for homotopy classification problems, particularly for the classification of homotopy types and for the computation of the group homotopy equivalences. Applications and examples of such computations are given, including when the fundamental group is non-trivial. Moreover, the deep connection between the homotopy classification problems and the cohomology theory of small categories is demonstrated. The prerequisites of the book are few: elementary topology and algebra. Consequently, this account will be valuable for non-specialists and experts alike. It is an important supplement to the standard presentations of algebraic topology, homotopy theory, category theory and homological algebra.
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Multiple Dirichlet Series, L-functions and Automorphic Forms

Author: Daniel Bump,Solomon Friedberg,Dorian Goldfeld

Publisher: Springer

ISBN: 0817683348

Category: Mathematics

Page: 361

View: 8677

Multiple Dirichlet Series, L-functions and Automorphic Forms gives the latest advances in the rapidly developing subject of Multiple Dirichlet Series, an area with origins in the theory of automorphic forms that exhibits surprising and deep connections to crystal graphs and mathematical physics. As such, it represents a new way in which areas including number theory, combinatorics, statistical mechanics, and quantum groups are seen to fit together. The volume also includes papers on automorphic forms and L-functions and related number-theoretic topics. This volume will be a valuable resource for graduate students and researchers in number theory, combinatorics, representation theory, mathematical physics, and special functions. Contributors: J. Beineke, B. Brubaker, D. Bump, G. Chinta, G. Cornelissen, C.A. Diaconu, S. Frechette, S. Friedberg, P. Garrett, D. Goldfeld, P.E. Gunnells, B. Heim, J. Hundley, D. Ivanov, Y. Komori, A.V. Kontorovich, O. Lorscheid, K. Matsumoto, P.J. McNamara, S.J. Patterson, M. Suzuki, H. Tsumura.
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Eisenstein Series and Automorphic Representations

With Applications in String Theory

Author: Philipp Fleig,Henrik P. A. Gustafsson,Axel Kleinschmidt,Daniel Persson

Publisher: N.A

ISBN: 1107189926

Category: Mathematics

Page: 575

View: 9957

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

Author: Daniel Bump

Publisher: Cambridge University Press

ISBN: 9780521658188

Category: Mathematics

Page: 574

View: 2341

This book takes advanced graduate students from the foundations to topics on the research frontier.
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Automorphic Representations and L-Functions for the General Linear Group:

Author: Dorian Goldfeld,Joseph Hundley

Publisher: Cambridge University Press

ISBN: 1139503081

Category: Mathematics

Page: N.A

View: 2013

This graduate-level textbook provides an elementary exposition of the theory of automorphic representations and L-functions for the general linear group in an adelic setting. Definitions are kept to a minimum and repeated when reintroduced so that the book is accessible from any entry point, and with no prior knowledge of representation theory. The book includes concrete examples of global and local representations of GL(n), and presents their associated L-functions. In Volume 1, the theory is developed from first principles for GL(1), then carefully extended to GL(2) with complete detailed proofs of key theorems. Several proofs are presented for the first time, including Jacquet's simple and elegant proof of the tensor product theorem. In Volume 2, the higher rank situation of GL(n) is given a detailed treatment. Containing numerous exercises by Xander Faber, this book will motivate students and researchers to begin working in this fertile field of research.
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An Introduction to Lie Groups and Lie Algebras

Author: Alexander Kirillov

Publisher: Cambridge University Press

ISBN: 0521889693

Category: Mathematics

Page: 222

View: 9532

This book is an introduction to semisimple Lie algebras; concise and informal, with numerous exercises and examples.
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p-adic Differential Equations

Author: Kiran S. Kedlaya

Publisher: Cambridge University Press

ISBN: 1139489208

Category: Mathematics

Page: N.A

View: 6959

Over the last 50 years the theory of p-adic differential equations has grown into an active area of research in its own right, and has important applications to number theory and to computer science. This book, the first comprehensive and unified introduction to the subject, improves and simplifies existing results as well as including original material. Based on a course given by the author at MIT, this modern treatment is accessible to graduate students and researchers. Exercises are included at the end of each chapter to help the reader review the material, and the author also provides detailed references to the literature to aid further study.
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Modern Analysis of Automorphic Forms By Example

Author: Paul Garrett

Publisher: Cambridge University Press

ISBN: 1107154006

Category: Mathematics

Page: 500

View: 7437

Volume 1 of a two-volume introduction to the analytical aspects of automorphic forms, featuring proofs of critical results with examples.
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Equivalents of the Riemann Hypothesis: Volume 2, Analytic Equivalents

Author: Kevin Broughan

Publisher: Cambridge University Press

ISBN: 1108187021

Category: Mathematics

Page: N.A

View: 6115

The Riemann hypothesis (RH) is perhaps the most important outstanding problem in mathematics. This two-volume text presents the main known equivalents to RH using analytic and computational methods. The book is gentle on the reader with definitions repeated, proofs split into logical sections, and graphical descriptions of the relations between different results. It also includes extensive tables, supplementary computational tools, and open problems suitable for research. Accompanying software is free to download. These books will interest mathematicians who wish to update their knowledge, graduate and senior undergraduate students seeking accessible research problems in number theory, and others who want to explore and extend results computationally. Each volume can be read independently. Volume 1 presents classical and modern arithmetic equivalents to RH, with some analytic methods. Volume 2 covers equivalences with a strong analytic orientation, supported by an extensive set of appendices containing fully developed proofs.
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Equivalents of the Riemann Hypothesis: Volume 1, Arithmetic Equivalents

Author: Kevin Broughan

Publisher: Cambridge University Press

ISBN: 1108195415

Category: Mathematics

Page: N.A

View: 8277

The Riemann hypothesis (RH) is perhaps the most important outstanding problem in mathematics. This two-volume text presents the main known equivalents to RH using analytic and computational methods. The book is gentle on the reader with definitions repeated, proofs split into logical sections, and graphical descriptions of the relations between different results. It also includes extensive tables, supplementary computational tools, and open problems suitable for research. Accompanying software is free to download. These books will interest mathematicians who wish to update their knowledge, graduate and senior undergraduate students seeking accessible research problems in number theory, and others who want to explore and extend results computationally. Each volume can be read independently. Volume 1 presents classical and modern arithmetic equivalents to RH, with some analytic methods. Volume 2 covers equivalences with a strong analytic orientation, supported by an extensive set of appendices containing fully developed proofs.
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Automorphic Forms and L-functions: Local aspects

Author: Stephen S. Gelbart

Publisher: American Mathematical Soc.

ISBN: 0821847082

Category: Mathematics

Page: 313

View: 3975

This book is the second of two volumes, which represent leading themes of current research in automorphic forms and representation theory of reductive groups over local fields. Articles in this volume mainly represent global aspects of automorphic forms. Among the topics are 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. The articles are written by leading researchers in the field, and bring the reader, advanced graduate students and researchers alike, to the frontline of the vigorous research in these deep, vital topics. The companion volume (""Contemporary Mathematics, Volume 488"") is devoted to global aspects of automorphic forms.
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Reversibility in Dynamics and Group Theory

Author: Anthony G. O'Farrell,Ian Short

Publisher: Cambridge University Press

ISBN: 1107442885

Category: Mathematics

Page: 292

View: 5885

An accessible yet systematic account of reversibility that demonstrates its impact throughout many diverse areas of mathematics.
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Number Theory, Analysis and Geometry

In Memory of Serge Lang

Author: Dorian Goldfeld,Jay Jorgenson,Peter Jones,Dinakar Ramakrishnan,Kenneth Ribet,John T. Tate

Publisher: Springer Science & Business Media

ISBN: 1461412609

Category: Mathematics

Page: 704

View: 9069

Serge Lang was an iconic figure in mathematics, both for his own important work and for the indelible impact he left on the field of mathematics, on his students, and on his colleagues. Over the course of his career, Lang traversed a tremendous amount of mathematical ground. As he moved from subject to subject, he found analogies that led to important questions in such areas as number theory, arithmetic geometry, and the theory of negatively curved spaces. Lang's conjectures will keep many mathematicians occupied far into the future. In the spirit of Lang’s vast contribution to mathematics, this memorial volume contains articles by prominent mathematicians in a variety of areas of the field, namely Number Theory, Analysis, and Geometry, representing Lang’s own breadth of interest and impact. A special introduction by John Tate includes a brief and fascinating account of the Serge Lang’s life. This volume's group of 6 editors are also highly prominent mathematicians and were close to Serge Lang, both academically and personally. The volume is suitable to research mathematicians in the areas of Number Theory, Analysis, and Geometry.
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