Mathematics 540: Topics in Analytic Number Theory

Spring 2004

Instructor: I. Laba. Office: Math Bldg 239. Phone: 822 2450. E-mail:

The course has been rescheduled to meet on Tuesdays and Thursdays 2 - 4, except that we do not meet on those Thursdays on which the Number Theory seminar is scheduled.

The general theme of this course will be "applications of Fourier analysis in number theory". This will include topics in combinatorial and additive number theory (Roth's theorem, Freiman's theorem) as well as more classical analytic number theory (Hardy-Littlewood circle method, Weyl's inequality). I am hoping to finish the course by presenting Vinogradov's three-primes theorem - this is more technical and complicated than the earlier topics, but it is also very interesting and should make for a satisfying conclusion.

There will be no final exam or midterms. Instead, each student taking this course for credit will be expected to present a short part of the course material (1-2 hours). The presentation topics can be chosen from the list below; if there is something else that you would like to present here, please discuss it with me in advance.

There is a lot of active research going on in this field. Accordingly, we will look at both classical results and some very recent work. While the focus will be firmly on number theory, there will be various bits of combinatorics and geometry mixed in. You may also expect guest presentations from a few faculty and visitors working on closely related topics.

Course outline (updated as of Feb. 22): This list of topics is not meant to be written in stone and may be modified according to demand - but only if you make a good case. The sources listed above are those that we are most likely to follow, but this should not prevent you from consulting other books and papers, such as those listed below and the references therein.

Lecture notes on the Web: