### MATH 5121: Topics in Complex Function Theory

**Description:** Advanced topics of contemporary interest. These include Riemann surfaces, Kleinian groups, entire functions, conformal mapping, several complex variables, and automorphic functions, among others. With a change of content this course may be repeatable to a maximum of twelve credits.

**Prerequisites:** MATH 5120.

**Credits:** 3

### MATH 5121 - Section 1: Analytic Number Theory

**Description:** In this course we will apply complex analysis to number theory, introducing the analytic machinery of Dirichlet series and modular forms and applying them to prove results about integers and prime numbers. Some classical theorems we treat will include the prime number theorem, Dirichlet's theorem on primes in arithmetic progression, and Jacobi's 4-square theorem. We'll also discuss the connection between modular forms and elliptic curves, and why the Riemann hypothesis is not so important (!) but its generalizations are.

**Prerequisites:** MATH 5120 and 5210. If you are missing one of these prerequisites and are still interested, speak with the instructor.

**Offered:** Fall

**Credits:** 3

**Sections: **Fall 2015 on Storrs Campus

PSCourseID | Course | Sec | Comp | Time | Room | Instructor |
---|---|---|---|---|---|---|

08312 | 5121 | 001 | Lecture | TuTh 12:30:00 PM-01:45:00 PM | MSB415 | Conrad, Keith |