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School of Environment and Society
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- Graduate major in Technology and Innovation Management
- Common courses
- Liberal arts and basic science courses
- Academic unit or major
- Graduate major in Mathematics
- Instructor(s)
- Ochiai Tadashi
- Class Format
- Lecture (Face-to-face)
- Media-enhanced courses
- Day/Period(Room No.)
- Thr5-6(M-103(H114))
- Group
- -
- Course number
- MTH.A407
- Credits
- 1
- Academic year
- 2023
- Offered quarter
- 3Q
- Syllabus updated
- 2023/3/20
- Lecture notes updated
- -
- Language used
- English
- Access Index
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Course description and aims
The theory of modular forms plays an important role in various aspects of the number theory. This course together with "Advanced Course in Algebra D1" given in 4Q forms one set of contents. In the first half "C1", we deal with the basics of the theory and we will deal with more advanced aspects of the theory in the latter half "D1".
Student learning outcomes
Students are expected to get familiar with the basic of the theory of modular forms and explicit examples.
Keywords
modular form, modular curve, L-function, Galois representation, automorphic representation
Competencies that will be developed
| ✔ Specialist skills | Intercultural skills | Communication skills | Critical thinking skills | Practical and/or problem-solving skills |
Class flow
Standard lecture course
Course schedule/Required learning
| Course schedule | Required learning | |
|---|---|---|
| Class 1 | Modular forms over the field of complex numbers: part 1 | Details will be provided during each class session |
| Class 2 | Modular forms over the field of complex numbers: part 2 | Details will be provided during each class session |
| Class 3 | Eichler--Shimura isomorphism | Details will be provided during each class session |
| Class 4 | Elliptic curves and modular curves: part 1 | Details will be provided during each class session |
| Class 5 | Elliptic curves and modular curves: part 2 | Details will be provided during each class session |
| Class 6 | The L-function of a modular form | Details will be provided during each class session |
| Class 7 | Algebraic definition of modular forms | Details will be provided during each class session |
Out-of-Class Study Time (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.
None required.
Assessment criteria and methods
Course scores are evaluated by homework assignments. Details will be announced during the course.
Related courses
- Algebra III
- MTH.A408 ： Advanced topics in Algebra D1
- ZUA.A334 ： Advanced courses in Algebra D
Prerequisites (i.e., required knowledge, skills, courses, etc.)
Mostly assuming only the basic knowledge of undergraduate mathematics
Other
None in particular.
