**Email**: kconrad at math dot uconn dot edu

**Lecture**: T/Th 5:30-6:45 in MONT 314

**Office Hours**: T 12:00-1:00, W 2:00-4:00 or by appointment in MONT 234

A brief introduction to characters of finite abelian groups.

A review of complex analysis.

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**Brief course 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 will treat include the prime number theorem, Dirichlet's theorem on primes in arithmetic progression, and Jacobi's 4-square theorem, and we'll discuss the connection between modular forms and elliptic curves.

**Prerequisites:** Familiarity with basic complex analysis and abstract algebra (mostly group theory).

**Homework:** There will be no graded assignments, but students are encouraged to work on exercises in the class notes. If you don't work on problems you won't learn the material well.