### 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: Topics in Complex Function Theory: 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 Riemann hypothesis and the connection between modular forms and elliptic curves.

**Prerequisites:** Familiarity with complex analysis (zeros, poles, residue theorem) and group theory. It would be sufficient to have taken Math 5120 (Complex Analysis) and 5210 (Abstract Algebra I), but if you have studied these topics elsewhere then please speak with the instructor about a permission number.

**Credits:** 3

**Sections: **Spring 2018 on Storrs Campus

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

15141 | 5121 | 001 | Lecture | TuTh 05:30:00 PM-06:45:00 PM | MONT314 | Conrad, Keith |