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

Course contents:

(1) Integer Points;
(2) Entire Functions of Finite Order;
(3) The Euler Gamma Function;
(4) The Riemann Zeta Function;
(5) The Connection Between the Sum of the Coefficients of a Dirichlet Series and the Function Defined by this Series;
(6) The Method of I.M.Vinogradov in the Theory of the Zeta Function;
(7) The Density of the Zeros of the Zeta Function and the Problem of the Distr-
ibution of Prime Numbers in Short Intervals;
(8) Dirichlet L-Functions;
(9) Prime Numbers in Arithmetic Progressions;
(10) The Goldbache Conjecture;
(11) Waring's Problem.

References:

(1) H. Davenport, Multiplicative Number Theory, Springer-Verlag, GTM74.
(2) A. A. Karatsuba, Basic Analytic Number Theory, Springer-Verlag.
(3) Pan Chengdong and Pan Chengbiao, Fundamentals of analytic number theory (in chinese), Science Press. Beijing 1991.