Classical
[Big_O] The Big-O and other important notation
[PN1] Introducing the Riemann zeta-function
[PN2] Integral functions of order one
[Gamma] A primer on the Gamma function
[PN3] More on zeta
[PN4] Perron's formula and the explicit formula
[PN5] The zero-free region and the prime number theorem
[PN6] Dirichlet characters
[PN7] Basic properties of Dirichlet L-functions
[PN8] Zero-free regions for Dirichlet L-functions, I
[PN9] Zero-free regions for Dirichlet L-functions, II
[PN10] The Siegel-Walfisz Theorem
Topics
[PN11] The Large Sieve
[PN12] The Selberg sieve applied to twin primes
These notes on the Selberg sieve were cribbed from some notes that I wrote about 4 years ago. These contain somewhat more material, which may be of interest to some of you.
In the last four lectures we proved Vinogradov's three primes theorem following Gowers. The notes (by Gowers) for this section of the course are here. Some of the notation is slightly different, and Lemmas 17,18 and Corollary 19 were not lectured and are not examinable.
Example Sheets