Ebook: Spectral Theory of Automorphic Functions and Its Applications

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Content:
Front Matter....Pages i-xiv
Introduction....Pages 1-4
What Does One Need Automorphic Functions For? Some Remarks for a Pragmatic Reader....Pages 5-8
Harmonic Analysis of Periodic Functions. The Hardy—Vorono? Formula....Pages 9-12
Expansion in Eigenfunctions of the Automorphic Laplacian on the Lobachevsky Plane....Pages 13-27
Harmonic Analysis of Automorphic Functions. Estimates for Fourier Coefficients of Parabolic Forms of Weight Zero....Pages 28-37
The Selberg Trace Formula for Fuchsian Groups of the First Kind....Pages 38-46
The Theory of the Selberg Zeta-Function....Pages 47-54
Problems in the Theory of the Discrete Spectrum of Automorphic Laplacians....Pages 55-70
The Spectral Moduli Problem....Pages 71-75
Automorphic Functions and the Kummer Problem....Pages 76-88
The Selberg Trace Formula on the Reductive Lie Groups....Pages 89-98
Automorphic Functions, Representations and L-Functions....Pages 99-107
Remarks and Comments. Annotations to the Cited Literature....Pages 108-118
Back Matter....Pages 119-176

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Content:
Front Matter....Pages i-xiv
Introduction....Pages 1-4
What Does One Need Automorphic Functions For? Some Remarks for a Pragmatic Reader....Pages 5-8
Harmonic Analysis of Periodic Functions. The Hardy—Vorono? Formula....Pages 9-12
Expansion in Eigenfunctions of the Automorphic Laplacian on the Lobachevsky Plane....Pages 13-27
Harmonic Analysis of Automorphic Functions. Estimates for Fourier Coefficients of Parabolic Forms of Weight Zero....Pages 28-37
The Selberg Trace Formula for Fuchsian Groups of the First Kind....Pages 38-46
The Theory of the Selberg Zeta-Function....Pages 47-54
Problems in the Theory of the Discrete Spectrum of Automorphic Laplacians....Pages 55-70
The Spectral Moduli Problem....Pages 71-75
Automorphic Functions and the Kummer Problem....Pages 76-88
The Selberg Trace Formula on the Reductive Lie Groups....Pages 89-98
Automorphic Functions, Representations and L-Functions....Pages 99-107
Remarks and Comments. Annotations to the Cited Literature....Pages 108-118
Back Matter....Pages 119-176
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