Spectral Theory of Automorphic Functions: and Its Applications / Edition 1

by A.B. Venkov

Overview

'Et moi, ..., si j'avait su comment en revcnrr, One service mathematics has rendered the je n'y serais point aile.' human race. It has put common sense back. Jules Verne where it belongs, on the topmost shelf next to the dusty canister labelled 'discarded non- The series is divergent; therefore we may be sense'. able to do something with it. Eric T. Bell O. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non- linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com- puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d'etre of this series.

Product Details

ISBN-13:	9780792304876
Publisher:	Springer Netherlands
Publication date:	10/31/1990
Series:	Mathematics and its Applications , #51
Edition description:	1990
Pages:	176
Product dimensions:	6.14(w) x 9.21(h) x 0.36(d)

Table of Contents

1. Introduction.- 2. What Does One Need Automorphic Functions for? Some Remarks or a Pragmatic Reader.- 3. Harmonic Analysis of Periodic Functions. The Hardy—Vorono? Formula.- 4. Expansion in Eigenfunctions of the Automorphic Laplacian on the Lobachevsky Plane.- 5. Harmonic Analysis of Automorphic Functions. Estimates for Fourier Coefficients of Parabolic Forms of Weight Zero.- 6. The Selberg Trace Formula for Fuchsian Groups of the First Kind.- 7. The Theory of the Selberg Zeta-Function.- 8. Problems in the Theory of the Discrete Spectrum of Automorphic Laplacians.- 9. The Spectral Moduli Problem.- 10. Automorphic Functions and the Kummer Problem.- 11. The Selberg Trace Formula on the Reductive Lie Groups.- 12. Automorphic Functions, Representations and L-functions.- 13. Remarks and Comments. Annotations to the Cited Literature.- References.- Appendix 1. Monodromy Groups and Automorphic Functions.- Appendix 2. Automorphic Functions for Effective Solutions of Certain Issues of the Riemann-Hilbert Problem.- Author Index.

Editorial Reviews

Vankov, of the Steklov Mathematical Institute, in Leningrad, explains the major concepts underlying various proofs and examines both classical and recent more advanced results. Topics covered include the expansion in automorphic eigenfunctions of Laplacians defined on symmetric Riemann spaces and the study of their spectra, Eisenstein series theory, Selberg zeta-function theory with applications to global problems in number theory, the theory of geometric and topological invariants of Riemannian manifolds, and classical monodromy theory. Translated from the Russian edition (date not stated). Annotation c. Book News, Inc., Portland, OR (booknews.com)

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