Analytic Number Theory - Fall 2019


Math 8440




Textbook:      There is no official textbook for the course, but I will use the following texts.

Description:  The aim of the course is to give an introduction to the analytic theory of the Riemann zeta and Dirichlet L-functions, the Prime Number Theorem in arithmetic progressions and applications such as Vinogradov's 3 prime theorem. We also discuss the Large Sieve and the Bombieri-Vinogradov theorem. Time permitted we discuss some more recent results concerning gaps between consecutive primes.
 

    
        Lecture Notes : Dirichlet Series, Riemann zeta function and the Prime Number Theorem

        Lecture 1-2        Lecture 3     Lecture 4     Lecture 5       

        2. Dirichlet L-functions

        Lecture 6     Lecture 7     Lecture 8   Lecture 9     Lecture 10    Lecture 11      Lecture 12       Lecture 13    Lecture 14-15

        3. The Prime Number Theorem in Arithmetic Progressions

        Lecture 15-16    Lecture 17      

        4. Ternary Goldbach problem, Vinogradov's 3-primes Theorem

        Lecture 18     Lecture 19    Lecture 20   

        5. The large Sieve and the Bombieri-Vinogradov Theorem

        Lecture 21      Lecture 22    Lecture 23