In number theory, L-functions are associated with various arithmetic objects. In this course, we explain the interpretation of L-functions based on Galois representations and discuss important results/conjectures on them. This course together with "Advanced Course in Algebra D1" given in 4Q forms one set of contents. Basic materials are dealt with in the first half "C1".
Students are expected to:
- understand fundamental notions and methods in algebraic number theory and Galois representation theory.
- understand the interpretation of L-functions based on Galois representation theory.
L-function, Euler product, Galois representation, Frobenius, Hasse-Weil Conjecture
✔ Specialist skills | Intercultural skills | Communication skills | Critical thinking skills | Practical and/or problem-solving skills |
This is a standard lecture course. There will be some assignments.
Course schedule | Required learning | |
---|---|---|
Class 1 | Various L-functions | Details will be provided during each class session |
Class 2 | Preparation from algebraic number theory | Details will be provided during each class session |
Class 3 | Galois representations | Details will be provided during each class session |
Class 4 | L-functions revisited | Details will be provided during each class session |
Class 5 | Weil Conjectures (Part 1) | Details will be provided during each class session |
Class 6 | Weil Conjectures (Part 2) | Details will be provided during each class session |
Class 7 | Drinfeld modules and t-motives | Details will be provided during each class session |
To enhance effective learning, students are encouraged to indulge themselves in L-functions and Galois representations.
None required.
None required.
Course scores are evaluated by homework assignments (100%). Details will be announced during the course.
Basic knowledge in undergraduate algebra