In the fall quarter (starting Sep 27) I will be teaching a graduate course on analytic prime number theory.  This will be similar to a graduate course I taught in 2015, and in particular will reuse several of the lecture notes from that course, though it will also incorporate some new material (and omit some material covered in the previous course, to compensate).  I anticipate covering the following topics:

  1. Elementary multiplicative number theory
  2. Complex-analytic multiplicative number theory
  3. The entropy decrement argument
  4. Bounds for exponential sums
  5. Zero density theorems
  6. Halasz’s theorem and the Matomaki-Radziwill theorem
  7. The circle method
  8. (If time permits) Chowla’s conjecture and the Erdos discrepancy problem [Update: I did not end up writing notes on this topic.]

Lecture notes for topics 3, 6, and 8 will be forthcoming.