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
Suggested books and references:
H. Davenport, Multiplicative Number Theory
,Springer GTM 74.
M. Ram Murty, Problems in Analytic Number Theory
,Springer GTM 206.
H. Iwaniec and E. Kowalski., Analytic Number Theory
,AMS Colloquium Publ. 53.