Time: the third Semester.
Credit: 3 hours.
Period: 54 hours.
Previous courses: Basic Analytic Number Theory,
                                 Classical Automorphic Forms

Course contents:

(1) Harmonic Analysis on the Hyperbolic Plane;
(2) Fuchsian Groups;
(3) Automorphic Forms;
(4) The Spectra; Theorem. Discrete Part;
(5) The automorphic Green Function;
(6) Analytic Continuation of Eisenstein Series;
(7) The Spectral Theorem. Continuous Part;
(8) Estimates for the Fourier Coefficients of Maass Forms;
(9) Spectral Theory of Kloosterman Sums;
(10) The Trace Formula;
(11) The Distribution of Eigenvalues;
(12) Hyperbolic Lattice-Point Problems;
(13) Spectral Bounds for Cusp Forms.

References:

(1) H. Iwaniec, Spectral methods of Automorphic Forms, Second Edtion, GSM      Volume53, Amer. Math. Soc., Providence, 2002.
(2) H. Iwaniec and E. Kowalski, Analytic Number Theorem, Amer. Math. Soc.       Colloquium Publ. 53, Amer. Math. Soc., Providence, 2004
(3) Yangbo Ye, Automorphic forms and trace formula, Peking University Press,       2001.