MATH524 THEORY OF FUNCTION FIELDS
| Course Code: | 2360524 |
| 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: | |
| Offered Semester: | Fall Semesters. |
Course Objectives
There are many analogies between number theory over algebraic number fields and over algebraic function fields. Our goal is to elaborate on these connections. The content of the course is relatively simple and essential to modern number theory and algebraic geometry.
Course Content
Valuations. Divisors, repartitions, differentials. Riemann-Roch Theorem. Rational function fields, elliptic and hyperelliptic function fields. Congruence zeta function, the functional equation for the L-functions.