Simple Algebras Base Change And The Advanced Theory Of The Trace Formula Am 120 Volume 120

Author : James Arthur,Laurent Clozel
Publisher : Princeton University Press
Page : 248 pages
File Size : 52,8 Mb
Release : 2016-03-02
Category : Mathematics
ISBN : 9781400882403

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Simple Algebras, Base Change, and the Advanced Theory of the Trace Formula. (AM-120), Volume 120 by James Arthur,Laurent Clozel Pdf

A general principle, discovered by Robert Langlands and named by him the "functoriality principle," predicts relations between automorphic forms on arithmetic subgroups of different reductive groups. Langlands functoriality relates the eigenvalues of Hecke operators acting on the automorphic forms on two groups (or the local factors of the "automorphic representations" generated by them). In the few instances where such relations have been probed, they have led to deep arithmetic consequences. This book studies one of the simplest general problems in the theory, that of relating automorphic forms on arithmetic subgroups of GL(n,E) and GL(n,F) when E/F is a cyclic extension of number fields. (This is known as the base change problem for GL(n).) The problem is attacked and solved by means of the trace formula. The book relies on deep and technical results obtained by several authors during the last twenty years. It could not serve as an introduction to them, but, by giving complete references to the published literature, the authors have made the work useful to a reader who does not know all the aspects of the theory of automorphic forms.

Author : James Arthur,Laurent Clozel
Publisher : Princeton, N.J. : Princeton University Press
Page : 230 pages
File Size : 48,6 Mb
Release : 1989
Category : Mathematics
ISBN : 069108517X

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Simple Algebras, Base Change, and the Advanced Theory of the Trace Formula by James Arthur,Laurent Clozel Pdf

A general principle, discovered by Robert Langlands and named by him the "functoriality principle," predicts relations between automorphic forms on arithmetic subgroups of different reductive groups. Langlands functoriality relates the eigenvalues of Hecke operators acting on the automorphic forms on two groups (or the local factors of the "automorphic representations" generated by them). In the few instances where such relations have been probed, they have led to deep arithmetic consequences. This book studies one of the simplest general problems in the theory, that of relating automorphic forms on arithmetic subgroups of GL(n, E) and GL(n, F) when E/F is a cyclic extension of number fields. (This is known as the base change problem for GL(n).) The problem is attacked and solved by means of the trace formula. The book relies on deep and technical results obtained by several authors during the last twenty years. It could not serve as an introduction to them, but, by giving complete references to the published literature, the authors have made the work useful to a reader who does not know all the aspects of the theory of automorphic forms.

Author : M. Ram Murty,V. Kumar Murty
Publisher : Springer Science & Business Media
Page : 185 pages
File Size : 48,9 Mb
Release : 2012-10-06
Category : Mathematics
ISBN : 9788132207696

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The Mathematical Legacy of Srinivasa Ramanujan by M. Ram Murty,V. Kumar Murty Pdf

Srinivasa Ramanujan was a mathematician brilliant beyond comparison who inspired many great mathematicians. There is extensive literature available on the work of Ramanujan. But what is missing in the literature is an analysis that would place his mathematics in context and interpret it in terms of modern developments. The 12 lectures by Hardy, delivered in 1936, served this purpose at the time they were given. This book presents Ramanujan’s essential mathematical contributions and gives an informal account of some of the major developments that emanated from his work in the 20th and 21st centuries. It contends that his work still has an impact on many different fields of mathematical research. This book examines some of these themes in the landscape of 21st-century mathematics. These essays, based on the lectures given by the authors focus on a subset of Ramanujan’s significant papers and show how these papers shaped the course of modern mathematics.

Author : Sirakov Boyan,Souza Paulo Ney De,Viana Marcelo
Publisher : World Scientific
Page : 5396 pages
File Size : 46,6 Mb
Release : 2019-02-27
Category : Mathematics
ISBN : 9789813272897

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Proceedings Of The International Congress Of Mathematicians 2018 (Icm 2018) (In 4 Volumes) by Sirakov Boyan,Souza Paulo Ney De,Viana Marcelo Pdf

The Proceedings of the ICM publishes the talks, by invited speakers, at the conference organized by the International Mathematical Union every 4 years. It covers several areas of Mathematics and it includes the Fields Medal and Nevanlinna, Gauss and Leelavati Prizes and the Chern Medal laudatios.

Author : Jörn Steuding
Publisher : Springer
Page : 322 pages
File Size : 49,8 Mb
Release : 2007-05-26
Category : Mathematics
ISBN : 9783540448228

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Value-Distribution of L-Functions by Jörn Steuding Pdf

These notes present recent results in the value-distribution theory of L-functions with emphasis on the phenomenon of universality. Universality has a strong impact on the zero-distribution: Riemann’s hypothesis is true only if the Riemann zeta-function can approximate itself uniformly. The text proves universality for polynomial Euler products. The authors’ approach follows mainly Bagchi's probabilistic method. Discussion touches on related topics: almost periodicity, density estimates, Nevanlinna theory, and functional independence.

Author : Sophie Morel
Publisher : Princeton University Press
Page : 231 pages
File Size : 48,8 Mb
Release : 2010-01-04
Category : Mathematics
ISBN : 9781400835393

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On the Cohomology of Certain Non-Compact Shimura Varieties (AM-173) by Sophie Morel Pdf

This book studies the intersection cohomology of the Shimura varieties associated to unitary groups of any rank over Q. In general, these varieties are not compact. The intersection cohomology of the Shimura variety associated to a reductive group G carries commuting actions of the absolute Galois group of the reflex field and of the group G(Af) of finite adelic points of G. The second action can be studied on the set of complex points of the Shimura variety. In this book, Sophie Morel identifies the Galois action--at good places--on the G(Af)-isotypical components of the cohomology. Morel uses the method developed by Langlands, Ihara, and Kottwitz, which is to compare the Grothendieck-Lefschetz fixed point formula and the Arthur-Selberg trace formula. The first problem, that of applying the fixed point formula to the intersection cohomology, is geometric in nature and is the object of the first chapter, which builds on Morel's previous work. She then turns to the group-theoretical problem of comparing these results with the trace formula, when G is a unitary group over Q. Applications are then given. In particular, the Galois representation on a G(Af)-isotypical component of the cohomology is identified at almost all places, modulo a non-explicit multiplicity. Morel also gives some results on base change from unitary groups to general linear groups.

Author : Rose Arny
Publisher : Unknown
Page : 1498 pages
File Size : 53,6 Mb
Release : 1989-05
Category : American literature
ISBN : UOM:39015033709554

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Forthcoming Books by Rose Arny Pdf

Author : Jonathan David Rogawski
Publisher : Princeton University Press
Page : 272 pages
File Size : 42,8 Mb
Release : 1990-09-21
Category : Mathematics
ISBN : 9780691085876

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Automorphic Representations of Unitary Groups in Three Variables by Jonathan David Rogawski Pdf

The purpose of this book is to develop the stable trace formula for unitary groups in three variables. The stable trace formula is then applied to obtain a classification of automorphic representations. This work represents the first case in which the stable trace formula has been worked out beyond the case of SL (2) and related groups. Many phenomena which will appear in the general case present themselves already for these unitary groups.

Author : Jonathan David Rogawski
Publisher : Princeton University Press
Page : 272 pages
File Size : 52,6 Mb
Release : 2016-03-02
Category : Mathematics
ISBN : 9781400882441

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Automorphic Representation of Unitary Groups in Three Variables. (AM-123), Volume 123 by Jonathan David Rogawski Pdf

The purpose of this book is to develop the stable trace formula for unitary groups in three variables. The stable trace formula is then applied to obtain a classification of automorphic representations. This work represents the first case in which the stable trace formula has been worked out beyond the case of SL (2) and related groups. Many phenomena which will appear in the general case present themselves already for these unitary groups.

Author : Stephen S. Gelbart
Publisher : American Mathematical Soc.
Page : 112 pages
File Size : 41,6 Mb
Release : 1996
Category : Selberg trace formula
ISBN : 9780821805718

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Lectures on the Arthur-Selberg Trace Formula by Stephen S. Gelbart Pdf

The Arthur-Selberg trace formula is an equality between two kinds of traces: the geometric terms given by the conjugacy classes of a group and the spectral terms given by the induced representations. In general, these terms require a truncation in order to converge, which leads to an equality of truncated kernels. The formulas are difficult in general and even the case of $GL$(2) is nontrivial. The book gives proof of Arthur's trace formula of the 1970s and 1980s, with special attention given to $GL$(2). The problem is that when the truncated terms converge, they are also shown to be polynomial in the truncation variable and expressed as ``weighted'' orbital and ``weighted'' characters. In some important cases the trace formula takes on a simple form over $G$. The author gives some examples of this, and also some examples of Jacquet's relative trace formula. This work offers for the first time a simultaneous treatment of a general group with the case of $GL$(2). It also treats the trace formula with the example of Jacquet's relative formula. Features: Discusses why the terms of the geometric and spectral type must be truncated, and why the resulting truncations are polynomials in the truncation of value $T$. Brings into play the significant tool of ($G, M$) families and how the theory of Paley-Weiner is applied. Explains why the truncation formula reduces to a simple formula involving only the elliptic terms on the geometric sides with the representations appearing cuspidally on the spectral side (applies to Tamagawa numbers). Outlines Jacquet's trace formula and shows how it works for $GL$(2).

Author : Anonim
Publisher : Unknown
Page : 1404 pages
File Size : 42,9 Mb
Release : 1985
Category : Monographic series
ISBN : STANFORD:36105015640464

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Books in Series by Anonim Pdf

Vols. for 1980- issued in three parts: Series, Authors, and Titles.

Author : Lynn Harold Loomis,Shlomo Sternberg
Publisher : World Scientific Publishing Company
Page : 596 pages
File Size : 49,6 Mb
Release : 2014-02-26
Category : Mathematics
ISBN : 9789814583954

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Advanced Calculus by Lynn Harold Loomis,Shlomo Sternberg Pdf

An authorised reissue of the long out of print classic textbook, Advanced Calculus by the late Dr Lynn Loomis and Dr Shlomo Sternberg both of Harvard University has been a revered but hard to find textbook for the advanced calculus course for decades. This book is based on an honors course in advanced calculus that the authors gave in the 1960's. The foundational material, presented in the unstarred sections of Chapters 1 through 11, was normally covered, but different applications of this basic material were stressed from year to year, and the book therefore contains more material than was covered in any one year. It can accordingly be used (with omissions) as a text for a year's course in advanced calculus, or as a text for a three-semester introduction to analysis. The prerequisites are a good grounding in the calculus of one variable from a mathematically rigorous point of view, together with some acquaintance with linear algebra. The reader should be familiar with limit and continuity type arguments and have a certain amount of mathematical sophistication. As possible introductory texts, we mention Differential and Integral Calculus by R Courant, Calculus by T Apostol, Calculus by M Spivak, and Pure Mathematics by G Hardy. The reader should also have some experience with partial derivatives. In overall plan the book divides roughly into a first half which develops the calculus (principally the differential calculus) in the setting of normed vector spaces, and a second half which deals with the calculus of differentiable manifolds.

Author : Clay Mathematics Institute. Summer School
Publisher : American Mathematical Soc.
Page : 708 pages
File Size : 40,5 Mb
Release : 2005
Category : Mathematics
ISBN : 082183844X

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Harmonic Analysis, the Trace Formula, and Shimura Varieties by Clay Mathematics Institute. Summer School Pdf

Langlands program proposes fundamental relations that tie arithmetic information from number theory and algebraic geometry with analytic information from harmonic analysis and group representations. This title intends to provide an entry point into this exciting and challenging field.

Author : Carlos J. Moreno
Publisher : American Mathematical Soc.
Page : 313 pages
File Size : 44,8 Mb
Release : 2005
Category : Algebraic number theory
ISBN : 9780821842669

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Advanced Analytic Number Theory: L-Functions by Carlos J. Moreno Pdf

Since the pioneering work of Euler, Dirichlet, and Riemann, the analytic properties of L-functions have been used to study the distribution of prime numbers. With the advent of the Langlands Program, L-functions have assumed a greater role in the study of the interplay between Diophantine questions about primes and representation theoretic properties of Galois representations. This book provides a complete introduction to the most significant class of L-functions: the Artin-Hecke L-functions associated to finite-dimensional representations of Weil groups and to automorphic L-functions of principal type on the general linear group. In addition to establishing functional equations, growth estimates, and non-vanishing theorems, a thorough presentation of the explicit formulas of Riemann type in the context of Artin-Hecke and automorphic L-functions is also given. The survey is aimed at mathematicians and graduate students who want to learn about the modern analytic theory of L-functions and their applications in number theory and in the theory of automorphic representations. The requirements for a profitable study of this monograph are a knowledge of basic number theory and the rudiments of abstract harmonic analysis on locally compact abelian groups.

Author : Anonim
Publisher : Unknown
Page : 2160 pages
File Size : 45,8 Mb
Release : 1993
Category : American literature
ISBN : UOM:39015016317664

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Subject Guide to Books in Print by Anonim Pdf