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catalog contributor b12638665.
catalog created "c2002.".
catalog date "2002".
catalog date "c2002.".
catalog dateCopyrighted "c2002.".
catalog description "5.1. Introduction -- 5.2. The Fourier expansion -- 5.3. An estimate for the automorphic Green function -- 5.4. Evaluation of some integrals -- Ch. 6. Analytic Continuation of the Eisenstein Series -- 6.1. The Fredholm equation for the Eisenstein series -- 6.2. The analytic continuation of E[subscript a](z,s) -- 6.3. The functional equations -- 6.4. Poles and residues of the Eisenstein series -- Ch. 7. The Spectral Theorem. Continuous Part -- 7.1. The Eisenstein transform -- 7.2. Bessel's inequality -- 7.3. Spectral decomposition of [epsilon]([Gamma]) -- 7.4. Spectral expansion of automorphic kernels -- Ch. 8. Estimates for the Fourier Coefficients of Maass Forms -- 8.1. Introduction -- 8.2. The Rankin-Selberg L-function -- 8.3. Bounds for linear forms -- 8.4. Spectral mean-value estimates -- 8.5. The case of congruence groups -- Ch. 9. Spectral Theory of Kloosterman Sums -- 9.1. Introduction -- 9.2. Analytic continuation of Z[subscript s](m,n) -- 9.3. Bruggeman-Kuznetsov formula -- ".
catalog description "9.4. Kloosterman sums formula -- 9.5. Petersson's formulas -- Ch. 10. The Trace Formula -- 10.1. Introduction -- 10.2. Computing the spectral trace -- 10.3. Computing the trace for parabolic classes -- 10.4. Computing the trace for the identity motion -- 10.5. Computing the trace for hyperbolic classes -- 10.6. Computing the trace for elliptic classes -- 10.7. Trace formulas -- 10.8. The Selberg zeta-function -- 10.9. Asymptotic law for the length of closed geodesics -- Ch. 11. The Distribution of Eigenvalues -- 11.1. Weyl's law -- 11.2. The residual spectrum and the scattering matrix -- 11.3. Small eigenvalues -- 11.4. Density theorems -- Ch. 12. Hyperbolic Lattice-Point Problems -- Ch. 13. Spectral Bounds for Cusp Forms -- 13.1. Introduction -- 13.2. Standard bounds -- 13.3. Applying the Hecke operator -- 13.4. Constructing an amplifier -- 13.5. The ergodicity conjecture -- App. A. Classical Analysis -- App. B. Special Functions.".
catalog description "Includes bibliographical references and index.".
catalog description "Preface to the AMS Edition -- Ch. 0. Harmonic Analysis on the Euclidean Plane -- Ch. 1. Harmonic Analysis on the Hyperbolic Plane -- 1.1. The upper half-plane -- 1.2. H as homogeneous space -- 1.3. The geodesic polar coordinates -- 1.4. Group decompositions -- 1.5. The classification of motions -- 1.6. The Laplace operator -- 1.7. Eigenfunctions of [Delta] -- 1.8. The invariant integral operators -- 1.9. The Green function on H -- Ch. 2. Fuchsian Groups -- 2.1. Definitions -- 2.2. Fundamental domains -- 2.3. Basic examples -- 2.4. The double coset decomposition -- 2.5. Kloosterman sums -- 2.6. Basic estimates -- Ch. 3. Automorphic Forms -- 3.1. Introduction -- 3.2. The Eisenstein series -- 3.3. Cusp forms -- 3.4. Fourier expansion of the Eisenstein series -- Ch. 4. The Spectral Theorem. Discrete Part -- 4.1. The automorphic Laplacian -- 4.2. Invariant integral operators of C([Gamma]) -- 4.3. Spectral resolution of [Delta] in C([Gamma]) -- Ch. 5. The Automorphic Green Function -- ".
catalog extent "xi, 220 p. :".
catalog identifier "0821831607 (acid-free paper)".
catalog isPartOf "Graduate studies in mathematics, 1065-7339 ; v. 53".
catalog issued "2002".
catalog issued "c2002.".
catalog language "eng".
catalog publisher "Providence, RI : American Mathematical Society,".
catalog subject "511.3/3 21".
catalog subject "Automorphic forms.".
catalog subject "Automorphic functions.".
catalog subject "QA353.A9 I88 2002".
catalog subject "Spectral theory (Mathematics)".
catalog tableOfContents "5.1. Introduction -- 5.2. The Fourier expansion -- 5.3. An estimate for the automorphic Green function -- 5.4. Evaluation of some integrals -- Ch. 6. Analytic Continuation of the Eisenstein Series -- 6.1. The Fredholm equation for the Eisenstein series -- 6.2. The analytic continuation of E[subscript a](z,s) -- 6.3. The functional equations -- 6.4. Poles and residues of the Eisenstein series -- Ch. 7. The Spectral Theorem. Continuous Part -- 7.1. The Eisenstein transform -- 7.2. Bessel's inequality -- 7.3. Spectral decomposition of [epsilon]([Gamma]) -- 7.4. Spectral expansion of automorphic kernels -- Ch. 8. Estimates for the Fourier Coefficients of Maass Forms -- 8.1. Introduction -- 8.2. The Rankin-Selberg L-function -- 8.3. Bounds for linear forms -- 8.4. Spectral mean-value estimates -- 8.5. The case of congruence groups -- Ch. 9. Spectral Theory of Kloosterman Sums -- 9.1. Introduction -- 9.2. Analytic continuation of Z[subscript s](m,n) -- 9.3. Bruggeman-Kuznetsov formula -- ".
catalog tableOfContents "9.4. Kloosterman sums formula -- 9.5. Petersson's formulas -- Ch. 10. The Trace Formula -- 10.1. Introduction -- 10.2. Computing the spectral trace -- 10.3. Computing the trace for parabolic classes -- 10.4. Computing the trace for the identity motion -- 10.5. Computing the trace for hyperbolic classes -- 10.6. Computing the trace for elliptic classes -- 10.7. Trace formulas -- 10.8. The Selberg zeta-function -- 10.9. Asymptotic law for the length of closed geodesics -- Ch. 11. The Distribution of Eigenvalues -- 11.1. Weyl's law -- 11.2. The residual spectrum and the scattering matrix -- 11.3. Small eigenvalues -- 11.4. Density theorems -- Ch. 12. Hyperbolic Lattice-Point Problems -- Ch. 13. Spectral Bounds for Cusp Forms -- 13.1. Introduction -- 13.2. Standard bounds -- 13.3. Applying the Hecke operator -- 13.4. Constructing an amplifier -- 13.5. The ergodicity conjecture -- App. A. Classical Analysis -- App. B. Special Functions.".
catalog tableOfContents "Preface to the AMS Edition -- Ch. 0. Harmonic Analysis on the Euclidean Plane -- Ch. 1. Harmonic Analysis on the Hyperbolic Plane -- 1.1. The upper half-plane -- 1.2. H as homogeneous space -- 1.3. The geodesic polar coordinates -- 1.4. Group decompositions -- 1.5. The classification of motions -- 1.6. The Laplace operator -- 1.7. Eigenfunctions of [Delta] -- 1.8. The invariant integral operators -- 1.9. The Green function on H -- Ch. 2. Fuchsian Groups -- 2.1. Definitions -- 2.2. Fundamental domains -- 2.3. Basic examples -- 2.4. The double coset decomposition -- 2.5. Kloosterman sums -- 2.6. Basic estimates -- Ch. 3. Automorphic Forms -- 3.1. Introduction -- 3.2. The Eisenstein series -- 3.3. Cusp forms -- 3.4. Fourier expansion of the Eisenstein series -- Ch. 4. The Spectral Theorem. Discrete Part -- 4.1. The automorphic Laplacian -- 4.2. Invariant integral operators of C([Gamma]) -- 4.3. Spectral resolution of [Delta] in C([Gamma]) -- Ch. 5. The Automorphic Green Function -- ".
catalog title "Spectral methods of automorphic forms / Henryk Iwaniec.".
catalog type "text".