### Lectures on the Arthur-Selberg Trace Formula

Number Theory and Automorphic Representations. Some problems in classical number theory, 1. Modular forms and automorphic representations; II. Selberg's Trace Formula 2. Historical Remarks, 2. Orbital integrals and Selberg's trace formula, 2. Three examples, 2.

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A necessary condition, 2. Generalizations and applications; III. Kernel Functions and the Convergence Theorem, 3. Preliminaries on GL r , 3.

Combinatorics and reduction theory, 3. The convergence theorem; IV. The Ad lic Theory, 4. Basic facts; V.

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The Geometric Theory, 5. A geometric I-function, 5. The weight functions; VI. The Geometric Expansionof the Trace Formula, 6. Weighted orbital integrals, 6. The unipotent distribution; VII.

The Spectral Theory, 7. A review of the Eisenstein series, 7.

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Cusp forms, truncation, the trace formula; VIII. The Invariant Trace Formula and its Applications, 8. The invariant trace formula for GL r , 8. Generalizations and applications; III. Kernel Functions and the Convergence Theorem, 3. Preliminaries on GL r , 3. Combinatorics and reduction theory, 3.

The convergence theorem; IV. The Ad lic Theory, 4. Basic facts; V. The Geometric Theory, 5. A geometric I-function, 5.

## ISBN 13: 9783540550211

The weight functions; VI. The Geometric Expansionof the Trace Formula, 6. Weighted orbital integrals, 6. The unipotent distribution; VII. The Spectral Theory, 7. A review of the Eisenstein series, 7.

Cusp forms, truncation, the trace formula; VIII. The Invariant Trace Formula and its Applications, 8. The invariant trace formula for GL r , 8.

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Applications and remarks. JavaScript is currently disabled, this site works much better if you enable JavaScript in your browser. Mathematics Number Theory and Discrete Mathematics. Lecture Notes in Mathematics Free Preview. Buy eBook.

Buy Softcover. FAQ Policy. About this book This book based on lectures given by James Arthur discusses the trace formula of Selberg and Arthur.