254A announcement: Analytic prime number theory

Bookmark Terence Tao’s site if you are interested in his notes on Analytic number theory! He will be placing lecture notes online on his blog.
This is a one-in-a-lifetime chance to learn Analytic Number Theory from a Master — Fields Medallist Terence Tao.

What's new

In the winter quarter (starting January 5) I will be teaching a graduate topics course entitled “An introduction to analytic prime number theory“. As the name suggests, this is a course covering many of the analytic number theory techniques used to study the distribution of the prime numbers $latex {{mathcal P} = {2,3,5,7,11,dots}}&fg=000000$. I will list the topics I intend to cover in this course below the fold. As with my previous courses, I will place lecture notes online on my blog in advance of the physical lectures.

The type of results about primes that one aspires to prove here is well captured by Landau’s classical list of problems:

  1. Even Goldbach conjecture: every even number $latex {N}&fg=000000$ greater than two is expressible as the sum of two primes.
  2. Twin prime conjecture: there are infinitely many pairs $latex {n,n+2}&fg=000000$ which are simultaneously prime.
  3. Legendre’s conjecture:…

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