Time: the second semester.
Credit: 3 hours.
Period: 54 hours.
Previous courses: Elementary Number Theory, Abstract Algebra, Basic Analytic                                  Number Theory.

Course contents:

(1) Introduction;
(2) The Classical Modular Forms;
(3) Automorphic Forms in General;
(4) The Eisentein and the Poincare Series;
(5) Kloosterman Sums;
(6) Bounds for the Fourier Coefficients of Cusp Forms;
(7) Hecke Operators;
(8) Autormophic L-Functions;
(9) Cusp Forms Associated with Elliptic Curves;
(10) Spherical Functions;
(11) Theta Functions;
(12) Representations by Quadratic Forms;
(13) Automorphic Forms Associated with Number Fields;
(14) Convolution L-Functions.

References:

(1) H. Iwaniec, Topics in the Classical Automorphic Forms, Graduate Studies in       Mathematics 17, Amer. Math. Soc, Providence, 1997.
(2) T. Miyake, Modular Forms, Springer-Verlag, 1989.
(3) G. Shimura, Introduction to the Arithmetic Theory of Automorphic Functions,       Princeton Univ. Press, Princeton NJ, 1971.
(4) Yangbo Ye, Modular forms and trace formula (in Chinese), Peking       University Press, 2001.