Fall 2023

Analytic Number Theory

Listed in: Mathematics and Statistics, as MATH-460


Amanda L. Folsom (Section 01)


This course is an introduction to Analytic Number Theory, a foundational subject in mathematics which dates back to the 1800s and is still a major research area today. The subject generally uses tools and techniques which are analytic in nature to solve problems primarily related to integers. Asymptotic and summation results and methods are of great significance in Analytic Number Theory. Two primary course objectives are to state and prove two major theorems: Dirichlet's Theorem on Primes in Arithmetic Progressions, and the Prime Number Theorem. In particular, we will study Selberg's "elementary" proof of the Prime Number Theorem. Additional topics may include: arithmetic functions, especially their averages, their asymptotics, and related summation formulae; Dirichlet convolutions; characters and Gauss sums; and an introduction to Dirichlet series, such as the Riemann zeta-function and L-functions. Further topics may vary.

Requisite: MATH 355. Limited to 25 students. Fall semester. Professor Folsom. 

How to handle overenrollment: Preference is given to seniors.

Students who enroll in this course will likely encounter and be expected to engage in the following intellectual skills, modes of learning, and assessment: Problem sets, In-class quizzes or exams, Take-home exams, In-class group work.

MATH 460 - LEC

Section 01
Tu 10:00 AM - 11:20 AM SMUD 207
Th 10:00 AM - 11:20 AM SMUD 207

This is preliminary information about books for this course. Please contact your instructor or the Academic Coordinator for the department, before attempting to purchase these books.

ISBN Title Publisher Author(s) Comment Book Store Price
Introduction to Analytic Number Theory Springer, Undergraduate Texts in Mathematics Apostol TBD


Other years: Offered in Fall 2023