Analytic Number Theory

Lior Silberman (University of British Columbia)

Jan 5, 2027 — Apr 27, 2027

About the course

We will count (that is, estimate the number of) integer and prime number solutions to equations. We will use combinatorial (“elementary”) methods, some Fourier analysis, and finally zeta-function (contour integration) techniques. Fourier analysis will be the unifying theme of the course. Possible topics include:

  1. Elementary techniques: Divisor sums; the Chebychev and Mertens estimates.
  2. Fourier analysis and exponential sums. Additive number theory.
  3. Smooth counting. Character sums.
  4. Dirichlet series and the Mellin transform; countour shifting.
  5. The Riemann zeta function; analytical continuation; the Prime Number Theorem.
  6. Dirichlet L-functions and the Prime Number Theorem in Arithmetic Progressions.

Registration

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.

Enrollment Details

Course Name
Analytic Number Theory
Date
Jan 5, 2027 — Apr 27, 2027
Course Number
MATH539
Section Number
201
Section Code
MATH539:201

Instructor(s)

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

Course Website

Availability

This course is available to students within the PIMS network, at universities beyond the PIMS network and from industry/government.

Lecture Schedule

  • Class: TTh 09:30-11:00 at ESB 4127 and on Zoom
  • Office Hours: Friday 10:30-11:30 and on zoom

Remote Access

Lectures will be held in-person on the UBC campus and on Zoom. Lectures will be recorded and the videos posted to an unlisted but openly accessible YouTube playlist. There will be Zoom office hours and a Piazza discussion board.

Grading

The final grade will be based on six to eight problem sets. There will be no final exam.

2026-2027