ANALYTIC NUMBER THEORY
An introduction to the Riemann zeta function and Dirichlet L-functions, and their application to topics such as the distribution of prime numbers and the arithmetic of quadratic fields. Familiarity with elementary number theory [such as MATH 567 ] and complex analysis [such as MATH 623 ] is strongly recommended.
Prerequisites & course information
Requisites: Graduate/professional standing or declared in Mathematics VISP (graduate or dissertator) Course Designation: Grad 50% - Counts toward 50% graduate coursework requirement Repeatable for Credit: No Last Taught: Fall 2026 Learning Outcomes: 1. Examine a range of mathematical proofs and identify underlyingprinciples and techniques. Audience: Graduate 2. Write clear and well-reasoned mathematical arguments. Audience: Graduate 3. Explain the methods used to establish the analytic continuation andfunctional equation of the Riemann zeta function and Dirichlet L-functions. Audience: Graduate 4. Apply tools from complex analysis to analyze the distribution ofzeros of L-functions. Audience: Graduate 5. Apply the above results on the zeros of L-functions to analyze thedistribution of prime numbers. Audience: Graduate Learning Outcomes: 1. Examine a range of mathematical proofs and identify underlyingprinciples and techniques. Audience: Graduate 2. Write clear and well-reasoned mathematical arguments. Audience: Graduate 3. Explain the methods used to establish the analytic continuation andfunctional equation of the Riemann zeta function and Dirichlet L-functions. Audience: Graduate 4. Apply tools from complex analysis to analyze the distribution ofzeros of L-functions. Audience: Graduate 5. Apply the above results on the zeros of L-functions to analyze thedistribution of prime numbers. Audience: Graduate
Sources
- Course catalogue ↗2026-2027