Lectures On The Arthur Selberg Trace Formula
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Lectures On The Arthur Selberg Trace Formula
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Author : Stephen S. Gelbart
language : en
Publisher: American Mathematical Soc.
Release Date : 1996
Lectures On The Arthur Selberg Trace Formula written by Stephen S. Gelbart 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 1996 with Selberg trace formula categories.
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).
The Selberg Arthur Trace Formula
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Author : Salahoddin Shokranian
language : en
Publisher: Springer
Release Date : 2006-11-14
The Selberg Arthur Trace Formula written by Salahoddin Shokranian 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.
This book based on lectures given by James Arthur discusses the trace formula of Selberg and Arthur. The emphasis is laid on Arthur's trace formula for GL(r), with several examples in order to illustrate the basic concepts. The book will be useful and stimulating reading for graduate students in automorphic forms, analytic number theory, and non-commutative harmonic analysis, as well as researchers in these fields. Contents: I. Number Theory and Automorphic Representations.1.1. Some problems in classical number theory, 1.2. Modular forms and automorphic representations; II. Selberg's Trace Formula 2.1. Historical Remarks, 2.2. Orbital integrals and Selberg's trace formula, 2.3.Three examples, 2.4. A necessary condition, 2.5. Generalizations and applications; III. Kernel Functions and the Convergence Theorem, 3.1. Preliminaries on GL(r), 3.2. Combinatorics and reduction theory, 3.3. The convergence theorem; IV. The Ad lic Theory, 4.1. Basic facts; V. The Geometric Theory, 5.1. The JTO(f) and JT(f) distributions, 5.2. A geometric I-function, 5.3. The weight functions; VI. The Geometric Expansionof the Trace Formula, 6.1. Weighted orbital integrals, 6.2. The unipotent distribution; VII. The Spectral Theory, 7.1. A review of the Eisenstein series, 7.2. Cusp forms, truncation, the trace formula; VIII.The Invariant Trace Formula and its Applications, 8.1. The invariant trace formula for GL(r), 8.2. Applications and remarks
The Selberg Arthur Trace Formula
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Author : Salahoddin Shokranian
language : en
Publisher:
Release Date : 2014-01-15
The Selberg Arthur Trace Formula written by Salahoddin Shokranian and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.
The Selberg Arthur Trace Formula
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Author : Salahoddin Shokranian
language : en
Publisher:
Release Date : 1992
The Selberg Arthur Trace Formula written by Salahoddin Shokranian and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with categories.
The Selberg Arthur Trace Formula
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Author : Salahoddin Shokranian
language : en
Publisher: Springer
Release Date : 1992-02-12
The Selberg Arthur Trace Formula written by Salahoddin Shokranian and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-02-12 with Mathematics categories.
This book based on lectures given by James Arthur discusses the trace formula of Selberg and Arthur. The emphasis is laid on Arthur's trace formula for GL(r), with several examples in order to illustrate the basic concepts. The book will be useful and stimulating reading for graduate students in automorphic forms, analytic number theory, and non-commutative harmonic analysis, as well as researchers in these fields. Contents: I. Number Theory and Automorphic Representations.1.1. Some problems in classical number theory, 1.2. Modular forms and automorphic representations; II. Selberg's Trace Formula 2.1. Historical Remarks, 2.2. Orbital integrals and Selberg's trace formula, 2.3.Three examples, 2.4. A necessary condition, 2.5. Generalizations and applications; III. Kernel Functions and the Convergence Theorem, 3.1. Preliminaries on GL(r), 3.2. Combinatorics and reduction theory, 3.3. The convergence theorem; IV. The Ad lic Theory, 4.1. Basic facts; V. The Geometric Theory, 5.1. The JTO(f) and JT(f) distributions, 5.2. A geometric I-function, 5.3. The weight functions; VI. The Geometric Expansionof the Trace Formula, 6.1. Weighted orbital integrals, 6.2. The unipotent distribution; VII. The Spectral Theory, 7.1. A review of the Eisenstein series, 7.2. Cusp forms, truncation, the trace formula; VIII.The Invariant Trace Formula and its Applications, 8.1. The invariant trace formula for GL(r), 8.2. Applications and remarks
The Selberg Trace Formula For Psl 2 R
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Author : Dennis A. Hejhal
language : en
Publisher: Springer
Release Date : 2006-11-15
The Selberg Trace Formula For Psl 2 R written by Dennis A. Hejhal and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.
The Selberg Trace Formula For Psl 2 R
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Author : Dennis A. Hejhal
language : en
Publisher: Springer
Release Date : 2006-11-14
The Selberg Trace Formula For Psl 2 R written by Dennis A. Hejhal 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.
Harmonic Analysis The Trace Formula And Shimura Varieties
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Author : Clay Mathematics Institute. Summer School
language : en
Publisher: American Mathematical Soc.
Release Date : 2005
Harmonic Analysis The Trace Formula And Shimura Varieties written by Clay Mathematics Institute. Summer School 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 2005 with Mathematics categories.
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.
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.
This book presents 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. Each of the twelve chapters focuses on a particular topic devoted to special cases of the program. The book is suitable for graduate students and researchers.
Lecture Notes In Mathematics
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Author :
language : en
Publisher:
Release Date : 1964
Lecture Notes In Mathematics written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1964 with Mathematics categories.