MATH525 ANALYTIC NUMBER THEORY
| Course Code: | 2360525 |
| METU Credit (Theoretical-Laboratory hours/week): | 3 (3.00 - 0.00) |
| ECTS Credit: | 8.0 |
| Department: | Mathematics |
| Language of Instruction: | English |
| Level of Study: | Graduate |
| Course Coordinator: | Assoc.Prof.Dr. ALİ ULAŞ ÖZGÜR KİŞİSEL |
| Offered Semester: | Fall Semesters. |
Course Objectives
The course aims to cover the classical theory of analytic methods in number theory. Particular emphasis is placed on the Riemann zeta function and how it is used to understand the distribution of prime numbers. In addition, L functions and their role in understanding primes in arithmetic progressions is discussed.
Course Content
Dirichlet series, Dirichlet L-functions, Chebychevs y and q functions, prime number theorem, distribution of primes, functional equations.
Course Learning Outcomes
At the end of the course the student is expected to:
- Relate properties of the Riemann zeta function and Dirichlet L-functions to the distribution of primes
- Use methods from complex analysis, in particular contour integration to obtain properties of the zeta function and L-functions.
- Prove equalities about infinite sums using Poisson's summation formula
- Infer results from the prime number theorem