Automorphic Forms

Time: the second semester

Course Classification: elective course

Credit: 3 hours

Period: 54 hours

Previous courses: Abstract Algebra, Complex Analysis

Syllabus:

(1) Introduction

(2) The classical modular forms

(3) Automorphic forms in general

(4) The Eisenstein and the Poincaré series

(5) Kloosterman sums

(6) Bounds for the Fourier coefficients of cusp forms

(7) Hecke operators

(8) Automorphic 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 inMathematics 17, Amer. Math. Soc., Providence, 1997.

(2) Y.Ye, Modular forms and trace formula (in Chinese), Peking University Press, 2001.