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Spectral Theory of Automorphic Functions : And Its Applications - A. B. Venkov

Spectral Theory of Automorphic Functions

And Its Applications

Hardcover Published: 31st October 1990
ISBN: 9780792304876
Number Of Pages: 176

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'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.

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.

ISBN: 9780792304876
ISBN-10: 079230487X
Series: Mathematics and Its Applications
Audience: General
Format: Hardcover
Language: English
Number Of Pages: 176
Published: 31st October 1990
Country of Publication: NL
Dimensions (cm): 23.39 x 15.6  x 1.27
Weight (kg): 0.45

Earn 374 Qantas Points
on this Book