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

Course contents:

(1) Elementary Theory of L-Functions Ⅰ;
(2) Elementary Theory of L-Functions Ⅱ;
(3) Classical Automorphic Forms;
(4) Artin L-Functions;
(5) L-Functions of Elliptic Curves and Modular Forms;
(6) Tate's Thesis;
(7) From Modular Forms to Automorphic Representations;
(8) Spectral Theory and the Trace Formula;
(9) Analytic Theory of L-Functions for GL(n);
(10) Langlands Conjecture for GL(n);
(11) Dual Groups and Langlands Functoriality;
(12) Informal Introduction to Geometric Langlands.

References:

(1) J. Bernstein, S. Gelbert (eds.), An Introduction to the Langlands Program,      BirkAauser, 2003.
(2) J. M. Cogdell, H. K. Kim, M. R. Murty, Lectures on Automorphic L-functions,      Amer. Math. Soc., Providence, 2004.
(3) R. Godement, H. Jacquet, Zeta functions of simple algebras, LNM, Vol. 260,      Springer-Verlag, Berlin-New York, 1972.
(4) D. Goldfeld, Automorphic Forms and L-Functions for the Group GL(n,R),      Cambridge Studies in Advanced Mathematics, No. 99, CUP, 2006.
(5) H. Iwaniec and E. Kowalski, Analytic Number Theory, Amer. Math. Soc. Collo-       quium Publ. 53, Amer. Math. Soc., Providence, 2004.
(6) C. J. Moreno, Advanced Analytic Number Theory: L-Functions, Mathematics       Surveys and Monographs, Vol. 115, Amer. Math. Soc., Providence, 2005.