L-functions

Time: the second semester

Course Classification: elective course

Credit: 3 hours

Period: 54 hours

Previous courses: Basic Analytic Number Theory, Automorphic Forms

Syllabus:

(1) The second-moment theory of families of L-functions

(2) Rankin-Selberg Methods

(3) Subconvexity bounds of L-functions

(4) Central values of L-functions

(5) Low-lying zeros of L-functions

References:

(1) V. Blomer, É. Fouvry, E. Kowalski, Ph. Michel, D. Milićević, and W. Sawin, The second-moment theory of families of L-functions, Mem. Amer. Math. Soc., 282(2023), Number 1394.

(2) J. M. Cogdell, H. K. Kim, M. R. Murty, Lectures on AutomorphicL-functions, Amer. Math. Soc., Providence, 2004.

(3) J. Bernstein, S. Gelbert (eds.), An Introduction to the Langlands Program, BirkAauser, 2003.

(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.