Time: the second semester.
Credit: 3 hours.
Period: 54 hours.
Previous courses: Elementary Number Theory, Complex Analysis, Basic                                  Analytic Number Theory

Course contents:

(1) Bilinear Forms and the Large Sieve;
(2) Exponential Sums;
(3) Elementary Sieve Methods;
(4) The Dirichlet Polynomials;
(5) Zero Density Estimates;
(6) Character Sums;
(7) The critical zeros of the Riemann zeta function;
(8) The spacing of zeros of the Riemann zeta-function;
(9) Central values of L-functions.

References:

(1) H. Iwaniec and E. Kowalski, Analytic number theory, American Mathematical      Society Colloquium Publications 53, American Mathematical Society, 2004.
(2) E. Bombieri, Le gran d crible dans la theorie analytique des nombres, societe      mathematique de France;
(3) Pan Chengdong and Pan Chengbiao, Fundamentals of analytic number
     theory (in Chinese), Science Press. Beijing 1991.