Spectral Decomposition And Eisenstein Series

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Spectral Decomposition And Eisenstein Series

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Author : Colette Moeglin
language : en
Publisher: Cambridge University Press
Release Date : 1995-11-02

Spectral Decomposition And Eisenstein Series written by Colette Moeglin and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-11-02 with Mathematics categories.

A self-contained introduction to automorphic forms, and Eisenstein series and pseudo-series, proving some of Langlands' work at the intersection of number theory and group theory.

The Meromorphic Continuation And Functional Equations Of Cuspidal Eisenstein Series For Maximal Cuspidal Subgroups

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Author : Shek-Tung Wong
language : en
Publisher: American Mathematical Soc.
Release Date : 1990

The Meromorphic Continuation And Functional Equations Of Cuspidal Eisenstein Series For Maximal Cuspidal Subgroups written by Shek-Tung Wong and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with Mathematics categories.

We carry out, in the context of an algebraic group and an arithmetic subgroup, an idea of Selberg for continuing Eisenstein series. It makes use of the theory of integral operators. The meromorphic continuation and functional equation of an Eisenstein series constructed with a cusp form on the Levi component of a rank one cuspidal subgroup are established.

On The Functional Equations Satisfied By Eisenstein Series

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Author : Robert P. Langlands
language : en
Publisher: Springer
Release Date : 2006-11-14

On The Functional Equations Satisfied By Eisenstein Series written by Robert P. Langlands and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.

Spectral Methods Of Automorphic Forms

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Author : Henryk Iwaniec
language : en
Publisher: American Mathematical Soc.
Release Date : 2002

Spectral Methods Of Automorphic Forms written by Henryk Iwaniec and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Mathematics categories.

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 volume was an underground classic, both as a textbook and as a respected source for results, ideas, and references. The book's reputation sparked a growing interest inthe mathematical community to bring it back into print. The AMS has answered that call with the publication of this second edition. In the book, Iwaniec treats the spectral theory of automorphic forms as the study of the space $L2 (H\Gamma)$, where $H$ is the upper half-plane and $\Gamma$ is a discretesubgroup of volume-preserving transformations of $H$. He combines various techniques from analytic number theory. Among the topics discussed are Eisenstein series, estimates for Fourier coefficients of automorphic forms, the theory of Kloosterman sums, the Selberg trace formula, and the theory of small eigenvalues. Henryk Iwaniec was awarded the 2002 AMS Cole Prize for his fundamental contributions to analytic number theory. Also available from the AMS by H. Iwaniec is Topics in ClassicalAutomorphic Forms, Volume 17 in the Graduate Studies in Mathematics series. The book is designed for graduate students and researchers working in analytic number theory.

Spectral Methods Of Automorphic Forms

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Author : Henryk Iwaniec
language : en
Publisher: American Mathematical Society, Revista Matemática Iberoamericana (RMI), Madrid, Spain
Release Date : 2021-11-17

Spectral Methods Of Automorphic Forms written by Henryk Iwaniec and has been published by American Mathematical Society, Revista Matemática Iberoamericana (RMI), Madrid, Spain this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-11-17 with Mathematics categories.

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.

The Genesis Of The Langlands Program

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Author : Julia Mueller
language : en
Publisher: Cambridge University Press
Release Date : 2021-08-05

The Genesis Of The Langlands Program written by Julia Mueller and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-08-05 with Mathematics categories.

A step-by-step guide to Langlands' early work leading up the Langlands Program for mathematicians and advanced students.

Harmonic Maass Forms And Mock Modular Forms Theory And Applications

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Author : Kathrin Bringmann
language : en
Publisher: American Mathematical Society
Release Date : 2025-02-24

Harmonic Maass Forms And Mock Modular Forms Theory And Applications written by Kathrin Bringmann and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-02-24 with Mathematics categories.

Modular forms and Jacobi forms play a central role in many areas of mathematics. Over the last 10–15 years, this theory has been extended to certain non-holomorphic functions, the so-called “harmonic Maass forms”. The first glimpses of this theory appeared in Ramanujan's enigmatic last letter to G. H. Hardy written from his deathbed. Ramanujan discovered functions he called “mock theta functions” which over eighty years later were recognized as pieces of harmonic Maass forms. This book contains the essential features of the theory of harmonic Maass forms and mock modular forms, together with a wide variety of applications to algebraic number theory, combinatorics, elliptic curves, mathematical physics, quantum modular forms, and representation theory.

Analysis Iv

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Author : Roger Godement
language : en
Publisher: Springer
Release Date : 2015-04-30

Analysis Iv written by Roger Godement and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-04-30 with Mathematics categories.

Analysis Volume IV introduces the reader to functional analysis (integration, Hilbert spaces, harmonic analysis in group theory) and to the methods of the theory of modular functions (theta and L series, elliptic functions, use of the Lie algebra of SL2). As in volumes I to III, the inimitable style of the author is recognizable here too, not only because of his refusal to write in the compact style used nowadays in many textbooks. The first part (Integration), a wise combination of mathematics said to be `modern' and `classical', is universally useful whereas the second part leads the reader towards a very active and specialized field of research, with possibly broad generalizations.

Automorphic Forms And Representations

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Author : Daniel Bump
language : en
Publisher: Cambridge University Press
Release Date : 1998-11-28

Automorphic Forms And Representations written by Daniel Bump and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-11-28 with Mathematics categories.

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

An Introduction To The Langlands Program

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Author : Joseph Bernstein
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-11

An Introduction To The Langlands Program written by Joseph Bernstein and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-11 with Mathematics categories.

For the past several decades the theory of automorphic forms has become a major focal point of development in number theory and algebraic geometry, with applications in many diverse areas, including combinatorics and mathematical physics. The twelve chapters of this monograph present a broad, user-friendly introduction to the Langlands program, that is, the theory of automorphic forms and its connection with the theory of L-functions and other fields of mathematics. Covered are a variety of areas in number theory from the classical zeta function up to the Langlands program. The exposition is sytematic, with each chapter focusing on a particular topic devoted to special cases of the program, and accessible to graduate students and researchers in the field.