Arithmetical functions, Primes in Arithmetic Progressions, Prime number theorem for arithmetic progressions and zeros of Dirichlet L-functions, Bombieri-Vinogradov theorem, Equidistribution, circle method and applications (ternary goldbach in mind), the Large Sieve and applications, Brun's theorem on twin primes.

(Further topics if time permits: more on sieves, automorpic forms and L-functions, Hecke's L-functions for number fields, bounds on exponential sum etc.)

Basic of number theory, compleX analysis, preferably some familiarity with MA 398 (Introduction to Anaytic number theroy).

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