Time: the third Semester.
Credit: 3 hours.
Period: 54 hours.
Previous courses: Elementary Number Theory, Complex Analysis, Basic Analytic Number Theory
Course contents:
(1) The Riemann zeta-function and Dirichlet L-functions;
(2) Sums of two squares, and two squares of primes;
(3) The large sieve;
(4) Exponential sums over primes I;
(5) The circle method in Warning-Goldbach problem;
(6) Sums of squares of primes;
(7) The major arcs in the Warning-Goldbach problem;
(8) Introduction to sieve methods;
(9) Exponential sums over primes Άς;
(10) Sums of cubes of primes;
(11) Sums of forth powers of primes;
(12) Sums of fifth powers of primes.
References:
(1) J. Y. Liu and T. Zhan, New development of the Additive theory of Prime Numbers, World Scientific Press, 2008.
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