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 LFunctions;
(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 LFunctions.
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, SpringerVerlag, 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.
