The Selberg Arthur Trace Formula

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 : 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 : 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 : M. Scott Osborne
Publisher : American Mathematical Soc.
ISBN 13 : 0821822837
Total Pages : 217 pages
Book Rating : 4.38/5 ( download)

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Download or read book The Selberg Trace Formula III: Inner Product Formulae (Initial Considerations) written by M. Scott Osborne and published by American Mathematical Soc.. This book was released on 1983 with total page 217 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Laurent Clozel
Publisher : International Pressof Boston Incorporated
ISBN 13 : 9781571462275
Total Pages : 527 pages
Book Rating : 4.79/5 ( download)

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Download or read book On the Stabilization of the Trace Formula written by Laurent Clozel and published by International Pressof Boston Incorporated. This book was released on 2011 with total page 527 pages. Available in PDF, EPUB and Kindle. Book excerpt:

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 : Isaac Y. Efrat
Publisher : American Mathematical Soc.
ISBN 13 : 0821824244
Total Pages : 121 pages
Book Rating : 4.45/5 ( download)

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Download or read book The Selberg Trace Formula for PSL_2(R)^n written by Isaac Y. Efrat and published by American Mathematical Soc.. This book was released on 1987 with total page 121 pages. Available in PDF, EPUB and Kindle. Book excerpt: We evaluate the Selberg trace formula for all discrete, irreducible, cofinite subgroups of PSL2 ([double-struck capital]R)[italic superscript]n. In particular, this involves studying the spectral theory of the fundamental domain, and the analysis of the appropriate Eisenstein series. A special role is played by the Hilbert modular groups, both because of their relation to the general case, stemming from a rigidity theorem, and their inherent algebraic number theoretic interest.

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