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The Selberg-Arthur Trace Formula

Based on Lectures by James Arthur

Salahoddin Shokranian (Autor)

Buch | Softcover

IX, 99 Seiten

1992
Springer Berlin (Verlag)
978-3-540-55021-1 (ISBN)

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This book based on lectures given by James Arthur discussesthe trace formula of Selberg and Arthur. The emphasis islaid on Arthur's trace formula for GL(r), with severalexamples in order to illustrate the basic concepts. The bookwill be useful and stimulating reading for graduate studentsin automorphic forms, analytic number theory, andnon-commutative harmonic analysis, as well as researchers inthese fields. Contents:I. Number Theory and Automorphic Representations.1.1. Someproblems in classical number theory, 1.2. Modular forms andautomorphic representations; II. Selberg's Trace Formula2.1. Historical Remarks, 2.2. Orbital integrals andSelberg's trace formula, 2.3.Three examples, 2.4. Anecessary condition, 2.5. Generalizations and applications;III. Kernel Functions and the Convergence Theorem, 3.1.Preliminaries on GL(r), 3.2. Combinatorics and reductiontheory, 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 theTrace Formula, 6.1. Weighted orbital integrals, 6.2. Theunipotent distribution; VII. The Spectral Theory, 7.1. Areview of the Eisenstein series, 7.2. Cusp forms,truncation, the trace formula; VIII.The Invariant TraceFormula and its Applications, 8.1. The invariant traceformula for GL(r), 8.2. Applications and remarks

Contents: Number Theory and Automorphic Representations: Some problems in classical number theory. Modular forms and automorphic representations.- Selberg's Trace Formula: Historical Remarks. Orbital integrals and Selberg's trace formula. Three examples. A necessary condition. Generalizations and applications.- Kernel Functions and the Convergence Theorem: Preliminaries on GL(r). Combinatorics and reduction theory. The convergence theorem.- The Adélic Theory: Basic facts.- The Geometric Theory: The JTO(f) and JT(f) distributions. A geometric I-function. The weight functions.- The Geometric Expansion of the Trace Formula: Weighted orbital integrals. The unipotent distribution.- The Spectral Theory: A review of the Eisenstein series. Cusp forms, truncation, the trace formula.- The Invariant Trace Formula and Its Applications: The in- variant trace formula for GL(r). Applications and remarks.- Bibliography.- Subject Index.

Erscheint lt. Verlag	12.2.1992
Reihe/Serie	Lecture Notes in Mathematics
Zusatzinfo	IX, 99 p.
Verlagsort	Berlin
Sprache	englisch
Maße	155 x 235 mm
Gewicht	176 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Arithmetik / Zahlentheorie
Themenwelt	Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
Schlagworte	automorphic forms • Calculus • Function • Harmonic Analysis • Invariant • Number Theory • Theorem
ISBN-10	3-540-55021-6 / 3540550216
ISBN-13	978-3-540-55021-1 / 9783540550211
Zustand	Neuware