Lectures On The Arthur Selberg Trace Formula

Author : Stephen S. Gelbart
Publisher : American Mathematical Soc.
ISBN 13 : 0821805711
Total Pages : 112 pages
Book Rating : 4.18/5 ( download)

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Download or read book Lectures on the Arthur-Selberg Trace Formula written by Stephen S. Gelbart and published by American Mathematical Soc.. This book was released on 1996 with total page 112 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Salahoddin Shokranian
Publisher : Springer
ISBN 13 : 3540466592
Total Pages : 104 pages
Book Rating : 4.98/5 ( download)

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Download or read book The Selberg-Arthur Trace Formula written by Salahoddin Shokranian and published by Springer. This book was released on 2006-11-14 with total page 104 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Author : Salahoddin Shokranian
Publisher :
ISBN 13 : 9783662173039
Total Pages : 108 pages
Book Rating : 4.34/5 ( download)

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Download or read book The Selberg-Arthur Trace Formula written by Salahoddin Shokranian and published by . This book was released on 2014-01-15 with total page 108 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Salahoddin Shokranian
Publisher :
ISBN 13 :
Total Pages : 97 pages
Book Rating : 4.86/5 ( download)

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Download or read book The Selberg-Arthur Trace Formula written by Salahoddin Shokranian and published by . This book was released on 1992 with total page 97 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Salahoddin Shokranian
Publisher : Springer
ISBN 13 : 9783540550211
Total Pages : 116 pages
Book Rating : 4.16/5 ( download)

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Download or read book The Selberg-Arthur Trace Formula written by Salahoddin Shokranian and published by Springer. This book was released on 1992-02-12 with total page 116 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Author : Dennis A. Hejhal
Publisher : Springer
ISBN 13 : 3540409149
Total Pages : 815 pages
Book Rating : 4.44/5 ( download)

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Download or read book The Selberg Trace Formula for PSL (2,R) written by Dennis A. Hejhal and published by Springer. This book was released on 2006-11-15 with total page 815 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Dennis A. Hejhal
Publisher : Springer
ISBN 13 : 3540379797
Total Pages : 523 pages
Book Rating : 4.99/5 ( download)

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Download or read book The Selberg Trace Formula for PSL (2,R) written by Dennis A. Hejhal and published by Springer. This book was released on 2006-11-14 with total page 523 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Dennis A. Hejhal
Publisher :
ISBN 13 :
Total Pages : 806 pages
Book Rating : 4.72/5 ( download)

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Download or read book The Selberg Trace Formula for Psl (2, Tr). Volume 2 written by Dennis A. Hejhal and published by . This book was released on 1983 with total page 806 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Clay Mathematics Institute. Summer School
Publisher : American Mathematical Soc.
ISBN 13 : 9780821838440
Total Pages : 708 pages
Book Rating : 4.4X/5 ( download)

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Download or read book Harmonic Analysis, the Trace Formula, and Shimura Varieties written by Clay Mathematics Institute. Summer School and published by American Mathematical Soc.. This book was released on 2005 with total page 708 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Joseph Bernstein
Publisher : Springer Science & Business Media
ISBN 13 : 0817682260
Total Pages : 283 pages
Book Rating : 4.62/5 ( download)

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Download or read book An Introduction to the Langlands Program written by Joseph Bernstein and published by Springer Science & Business Media. This book was released on 2013-12-11 with total page 283 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.