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 LFunctions;
(9) Prime Numbers in Arithmetic Progressions;
(10) The Goldbache Conjecture;
(11) Waring's Problem.
References:
(1) H. Davenport, Multiplicative Number Theory, SpringerVerlag, GTM74.
(2) A. A. Karatsuba, Basic Analytic Number Theory, SpringerVerlag.
(3) Pan Chengdong and Pan Chengbiao, Fundamentals of analytic number theory (in chinese), Science Press. Beijing 1991.
