The Selberg Arthur Trace Formula
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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.
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 : 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
On The Stabilization Of The Trace Formula
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Author : Laurent Clozel
language : en
Publisher:
Release Date : 2017-10-30
On The Stabilization Of The Trace Formula written by Laurent Clozel and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-10-30 with categories.
This is the first volume of a projected series of two or three collections of mainly expository articles on the arithmetic theory of automorphic forms. The books are intended primarily for two groups of readers. The first group is interested in the structure of automorphic forms on reductive groups over number fields, and specifically in qualitative information about the multiplicities of automorphic representations. The second group is interested in the problem of classifying l-adic representations of Galois groups of number fields. Langlands' conjectures elaborate on the notion that these two problems overlap to a considerable degree. The goal of this series of books is to gather into one place much of the evidence that this is the case, and to present it clearly and succinctly enough so that both groups of readers are not only convinced by the evidence but can pass with minimal effort between the two points of view. More than a decade's worth of progress toward the stabilization of the Arthur-Selberg trace formula, culminating in Ngô Bau Châu's recent proof of the Fundamental Lemma, has made this series timely.
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.
Relative Trace Formulas
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Author : Werner Müller
language : en
Publisher: Springer Nature
Release Date : 2021-05-18
Relative Trace Formulas written by Werner Müller and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-05-18 with Mathematics categories.
A series of three symposia took place on the topic of trace formulas, each with an accompanying proceedings volume. The present volume is the third and final in this series and focuses on relative trace formulas in relation to special values of L-functions, integral representations, arithmetic cycles, theta correspondence and branching laws. The first volume focused on Arthur’s trace formula, and the second volume focused on methods from algebraic geometry and representation theory. The three proceedings volumes have provided a snapshot of some of the current research, in the hope of stimulating further research on these topics. The collegial format of the symposia allowed a homogeneous set of experts to isolate key difficulties going forward and to collectively assess the feasibility of diverse approaches.
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 Iii Inner Product Formulae Initial Considerations
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Author : M. Scott Osborne
language : en
Publisher: American Mathematical Soc.
Release Date : 1983
The Selberg Trace Formula Iii Inner Product Formulae Initial Considerations written by M. Scott Osborne 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 1983 with Automorphic forms categories.
In this memoir, we lay the foundations for the study of inner product formulae, one of the key technical preliminaries in the derivation of the Selberg trace formula.