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