Automorphic Forms on GL (3,TR)

Automorphic Forms on GL (3,TR) PDF Author: D. Bump
Publisher: Springer
ISBN: 3540390553
Category : Mathematics
Languages : en
Pages : 196

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Automorphic Forms on GL (3,TR)

Automorphic Forms on GL (3,TR) PDF Author: D. Bump
Publisher: Springer
ISBN: 3540390553
Category : Mathematics
Languages : en
Pages : 196

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Book Description


Automorphic Forms, Representations and $L$-Functions

Automorphic Forms, Representations and $L$-Functions PDF Author: Armand Borel
Publisher: American Mathematical Soc.
ISBN: 0821814370
Category : Mathematics
Languages : en
Pages : 394

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Book Description
Part 2 contains sections on Automorphic representations and $L$-functions, Arithmetical algebraic geometry and $L$-functions

An Introduction to Automorphic Representations

An Introduction to Automorphic Representations PDF Author: Jayce R. Getz
Publisher: Springer Nature
ISBN: 3031411536
Category :
Languages : en
Pages : 611

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Automorphic Forms on GL (2)

Automorphic Forms on GL (2) PDF Author: H. Jacquet
Publisher: Springer
ISBN: 3540376127
Category : Mathematics
Languages : en
Pages : 156

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Representation Theory and Automorphic Forms

Representation Theory and Automorphic Forms PDF Author: Toshiyuki Kobayashi
Publisher: Springer Science & Business Media
ISBN: 0817646469
Category : Mathematics
Languages : en
Pages : 220

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Book Description
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.

Automorphic Forms on Adele Groups. (AM-83), Volume 83

Automorphic Forms on Adele Groups. (AM-83), Volume 83 PDF Author: Stephen S. Gelbart
Publisher: Princeton University Press
ISBN: 1400881617
Category : Mathematics
Languages : en
Pages : 227

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Book Description
This volume investigates the interplay between the classical theory of automorphic forms and the modern theory of representations of adele groups. Interpreting important recent contributions of Jacquet and Langlands, the author presents new and previously inaccessible results, and systematically develops explicit consequences and connections with the classical theory. The underlying theme is the decomposition of the regular representation of the adele group of GL(2). A detailed proof of the celebrated trace formula of Selberg is included, with a discussion of the possible range of applicability of this formula. Throughout the work the author emphasizes new examples and problems that remain open within the general theory. TABLE OF CONTENTS: 1. The Classical Theory 2. Automorphic Forms and the Decomposition of L2(PSL(2,R) 3. Automorphic Forms as Functions on the Adele Group of GL(2) 4. The Representations of GL(2) over Local and Global Fields 5. Cusp Forms and Representations of the Adele Group of GL(2) 6. Hecke Theory for GL(2) 7. The Construction of a Special Class of Automorphic Forms 8. Eisenstein Series and the Continuous Spectrum 9. The Trace Formula for GL(2) 10. Automorphic Forms on a Quaternion Algebr?

Automorphic Forms

Automorphic Forms PDF Author: Anton Deitmar
Publisher: Springer Science & Business Media
ISBN: 144714435X
Category : Mathematics
Languages : en
Pages : 255

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Book Description
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.

Introduction to the Arithmetic Theory of Automorphic Functions

Introduction to the Arithmetic Theory of Automorphic Functions PDF Author: Gorō Shimura
Publisher: Princeton University Press
ISBN: 9780691080925
Category : Mathematics
Languages : en
Pages : 292

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Book Description
The theory of automorphic forms is playing increasingly important roles in several branches of mathematics, even in physics, and is almost ubiquitous in number theory. This book introduces the reader to the subject and in particular to elliptic modular forms with emphasis on their number-theoretical aspects. After two chapters geared toward elementary levels, there follows a detailed treatment of the theory of Hecke operators, which associate zeta functions to modular forms. At a more advanced level, complex multiplication of elliptic curves and abelian varieties is discussed. The main question is the construction of abelian extensions of certain algebraic number fields, which is traditionally called "Hilbert's twelfth problem." Another advanced topic is the determination of the zeta function of an algebraic curve uniformized by modular functions, which supplies an indispensable background for the recent proof of Fermat's last theorem by Wiles.

Eisenstein Series and Automorphic Representations

Eisenstein Series and Automorphic Representations PDF Author: Philipp Fleig
Publisher: Cambridge Studies in Advanced
ISBN: 1107189926
Category : Mathematics
Languages : en
Pages : 587

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

Automorphic Forms and the Langlands Program

Automorphic Forms and the Langlands Program PDF Author: Lizhen Ji
Publisher: International Press of Boston
ISBN: 9781571461414
Category : Algebraic number theory
Languages : en
Pages : 0

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Book Description
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.