MA 350: Topics in Analytic Number Theory

Credits: 3:0

Pre-requisites :

1. Basics of number theory
2. Complex analysis
3. Preferably some familiarity with MA 352 (=Introduction to Analytic number theory)

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, automorphic forms and L-functions, Hecke’s L-functions for number fields, bounds on exponential sums etc.)

Suggested books and references:

1. H. Davenport, Multiplicative Number Theory, Springer GTM 74.
2. M. Ram Murty, Problems in Analytic Number Theory, Springer GTM 206.
3. H. Iwaniec and E. Kowalski., Analytic Number Theory, AMS Colloquium Publ. 53.

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