2023 Students Enrolled in or before 2015 School of Science Mathematics
Advanced courses in Algebra D
- Academic unit or major
- Mathematics
- Instructor(s)
- Tadashi Ochiai
- Class Format
- Lecture (Face-to-face)
- Media-enhanced courses
- -
- Day of week/Period
(Classrooms) - 5-6 Thu (M-103(H114))
- Class
- -
- Course Code
- ZUA.A334
- Number of credits
- 100
- Course offered
- 2023
- Offered quarter
- 4Q
- Syllabus updated
- Jul 8, 2025
- Language
- English
Syllabus
Course overview and goals
The theory of modular forms plays an essential role in various aspects of the number theory. Based on the basic facts on modular curves and modular forms explained in "Advanced Course in Algebra D1" in 3Q", we deal with the basics of the applications to the L-function and the Galois representation associated with a modular form.
Course description and aims
Students are expected to understand applications of the theory of modular forms and their relation to some other areas.
Keywords
modular form, modular curve, L-function, Galois representation, automorphic representation
Competencies
- Specialist skills
- Intercultural skills
- Communication skills
- Critical thinking skills
- Practical and/or problem-solving skills
Class flow
Standard lecture course
Course schedule/Objectives
| Course schedule | Objectives | |
|---|---|---|
| Class 1 | Galois representation associated to a cuspform: part 1 | Details will be provided during each class session |
| Class 2 | Galois representation associated to a cuspform: part 2 | Details will be provided during each class session |
| Class 3 | Modular forms and automorphic representations: part 1 | Details will be provided during each class session |
| Class 4 | Modular forms and automorphic representations: part 2 | Details will be provided during each class session |
| Class 5 | Automorphic representations and the Langlands correspondence | Details will be provided during each class session |
| Class 6 | Advanced topics: part 1 | Details will be provided during each class session |
| Class 7 | Advanced topics: part 2 | Details will be provided during each class session |
Study advice (preparation and review)
To enhance effective learning, students are encouraged to explore references provided in lectures and other materials.
Textbook(s)
None required.
Reference books, course materials, etc.
Neal Koblitz, Introduction to Elliptic Curves and Modular forms, GTM 97, Springer-Verlag, New York, 1993
Toshitsune Miyake, Modular Forms, english ed., Springer Monographs in Mathematics, Springer-Verlag, Berlin 2006
Evaluation methods and criteria
Course scores are evaluated by homework assignments. Details will be announced during the course.
Related courses
- ZUA.A333 ： Advanced courses in Algebra C
Prerequisites
Some knowledge of Algebraic Geometry might be assumed, but try to talk so that the participants can follow the contents without this knowledge
Other
None in particular.