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¢ń£»
(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, An Introduction to the Langlands rogram,BirkAauser, 2003.
(2) J. M. Cogdell, H. K. Kim, M. R. Murty, Lectures on Automorphic L-functions, Amer. Math. Soc., Providence, 2004.
(3) H. Iwaniec and E. Kowalski, Analytic Number Theory, Amer. Math. Soc. Collo- quium Publ. 53, Amer. Math. Soc., Providence, 2004.
(4) C. J. Moreno, Advanced Analytic Number Theory: L-Functions, Mathematics Surveys and Monographs, Vol. 115, Amer. Math. Soc., Providence, 2005.
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