- Lectures will be physically held in room ESB 4133 (Earth Sciences Building), and will be simultaneously broadcast on Zoom
- Zoom link has been emailed to students (please don't distribute widely)
Office hours: right after class, or by appointment
- I can meet with students either physically in room MATH 212 (Mathematics Building), or on Zoom at the same URL as the lectures
Email address: gerg@math.ubc.ca
This course is a second graduate course in number theory, intended to follow Analytic Number Theory I which is taught by Prof. Habiba Kadiri (University of Lethbridge) in Fall 2022. This course also precedes the summer school Inclusive Paths in Explicit Number Theory in Summer 2023 and is designed to give students the ideal preparation for that summer school program. All three of these events are part of the current PIMS Collaborative Research Group
After a quick review of the prime number theorem and the “explicit formula”, we will start by learning about Dirichlet characters and sums involving them (character sums over intervals and Gauss sums), which is sufficient preparation to prove Dirichlet's theorem on the infinitude of primes in arithmetic progressions. We will then study Dirichlet
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 for ψ( The evaluation for this course will consist of regular attendance and of 1–2 write-ups (5–10 pages) of specific topics or results related to the subject matter, which will be completed either individually or in teams depending on the enrollment in the course.
- For non-UBC students registering for Analytic Number Theory II (this course, MATH 613D at UBC), we must receive the completed form by November 15, so I encourage you to fill out the form and start the chain of authorizations by October 31.
- Non-UBC students who take this course will be given a UBC email address—make sure you forward it to an email account you check regularly. Your grade for this course will not appear on your school's transcript (I believe) but rather you will get a separate UBC transcript for this course.
- The UBC mathematics department has a process by which undergraduate students can apply to take our graduate courses (inquire with the Graduate Program Coordinator in our office). However, I don't believe that undergraduate students are eligible for credit for courses at other universities through WDA. I am certainly open to students unofficially auditing my lectures, and I believe Prof. Kadiri feels the same about Analytic Number Theory I.
- The Western Deans Agreement applies to students from certain universities (mostly in western Canada). However, other students can also take this course through UBC's Graduate Exchange Agreement or through non-exchange visitor status.
- H. L. Montgomery and R. C. Vaughan,
*Multiplicative Number Theory I. Classical Theory* - H. Iwaniec and E. Kowalski,
*Analytic Number Theory* - P. T. Bateman and H. G. Diamond,
*Analytic Number Theory: An introductory course* - H. Davenport,
*Multiplicative Number Theory* - T. M. Apostol,
*Introduction to Analytic Number Theory*
- I. Niven, H. S. Zuckerman, and H. L. Montgomery,
*An Introduction to the Theory of Numbers* - G. H. Hardy and E. M. Wright,
*An Introduction to the Theory of Numbers*
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