Math 808 - Analytic Number Theory
Course Description

Probable topics:
  • Prime number theorem
  • Zeros of zeta
  • Explicit formulas and applications
  • Computing π(x)
  • Siegel zeros
  • Sieve methods (Goldbach, ...)
  • Gaps between primes (Zhang, Maynard, Tao)

    Textbook:


    There is no textbook. I'll partly follow
  • Davenport, Multiplicative Number Theory
    and
  • Online notes by Elkies

    Other books that I might use include
  • Prachar, Primzahlverteilung
  • Bateman and Diamond, Analytic Number Theory
  • Estermann, Introduction to Modern Prime Number Theory

    Prerequisites:

    Elementary complex analysis (Cauchy's theorem, residue theorem), Beginning real analysis (probaby Math 411 suffices), Elementary number theory.

    Room:

    Math 0305

    Time:

    MWF 1:00-1:50