Basic Analytic Number Theory

Time: the first semester

Course Classification: compulsory course

Credit:3 hours

Period:54 hours

Previous courses: Elementary Number Theory, Complex Analysis

Syllabus:

(1) Integer Points

(2) Entire Functions of Finite Order

(3) The Euler Gamma Function

(4) The Riemann Zeta Function

(5) The Prime Number Theorem

(6) The Method of I.M.Vinogradov

(7) Zero Density Estimates

(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, GTM 74.

(2) A. A. Karatsuba, Basic Analytic Number Theory, Springer-Verlag.