Comparative Prime Number TheoryGreg Martin (University of British Columbia)
Jan 1, 2021 — Jun 1, 2021
About the course
We will begin with a quick review of the prime number theorem and the “explicit formula”, then develop the theory of Dirichlet characters, and combine these two sets of tools to prove the prime number theorem in arithmetic progressions. We will then move into comparing two counting functions of primes in arithmetic progressions, going through the history of such comparisons and learning how the normalized difference can be modeled by random variables, thus giving us a way to understand its limiting distribution. Student assessment will consist of some modest combination of presentations and reviews of research articles.
Recommended prerequisites are a solid course (preferably graduate-level) in elementary number theory, and a graduate-level course in analytic number theory, one that included a proof of the prime number theorem and the corresponding explicit formula. An undergraduate course in probability would also be helpful. Reference texts would be standard analytic number theory books by Iwaniec & Kowalski, by Montgomery & Vaughan, and by Titchmarsh. Students who are willing to learn some of this background as they go are welcome.
Classes will be held live (synchronously) on Zoom and regular attendance will be important. The current tentative schedule is to meet at 10am Pacific time on Mondays and Wednesdays and possibly Fridays. Students can join from any physical location.
This course is available for registration under the Western Dean's Agreement. To register, you must obtain the approval of the course instructor and you must complete the Western Dean's agreement form , using the details below. The completed form should be signed by your home institution department and school of graduate studies, then returned to the host institution of the course.
- Course Name
- Comparative Prime Number Theory
- Jan 1, 2021 — Jun 1, 2021
- Course Number
- MATH 613D
- Section Number
- Section Code
University of British Columbia
For help with completing the Western Dean’s agreement form, please contact the graduate student program coordinator at your institution. For more information about the agreement, please see the Western Dean's Agreement website
Other Course Details
Reference texts would be standard analytic number theory books by Iwaniec & Kowalski, by Montgomery & Vaughan, and by Titchmarsh.