2021 Faculty Courses School of Science Department of Mathematics Graduate major in Mathematics
Advanced topics in Algebra H1
- Academic unit or major
- Graduate major in Mathematics
- Instructor(s)
- Masatoshi Suzuki
- Class Format
- Lecture
- Media-enhanced courses
- -
- Day of week/Period
(Classrooms) - 5-6 Mon
- Class
- -
- Course Code
- MTH.A508
- Number of credits
- 100
- Course offered
- 2021
- Offered quarter
- 4Q
- Syllabus updated
- Jul 10, 2025
- Language
- English
Syllabus
Course overview and goals
The theory of automorphic L-functions is a major research area of modern number theory, and is nowadays becoming more and more important in several related areas of mathematics. This lecture aims to explain the basics of automorphic L-functions and to mention a recent breakthrough on the subconvexity problem. This lecture is based on Advanced topics in Algebra G1.
Course description and aims
Students are expected to:
- obtain basic notions and methods related to automorphic L-functions,
- understand modern tools and concepts in the theory of automorphic L-functions,
- attain a deep understanding of the theory of automorphic L-functions.
Keywords
modular forms, automorphic representations, automorphic L-functions, subconvexity problem
Competencies
- Specialist skills
- Intercultural skills
- Communication skills
- Critical thinking skills
- Practical and/or problem-solving skills
Class flow
This is a standard lecture course. There will be some homework assignments.
Course schedule/Objectives
| Course schedule | Objectives | |
|---|---|---|
| Class 1 | Automorphic representations of GL(n) | Details will be provided during each class session |
| Class 2 | Integral representations of automorphic L-functions | Details will be provided during each class session |
| Class 3 | Eisenstein series and the Rankin-Selberg method | Details will be provided during each class session |
| Class 4 | Spectral decomposition | Details will be provided during each class session |
| Class 5 | Reduction from GL(2)×GL(2) to GL(2)×GL(1) | Details will be provided during each class session |
| Class 6 | Adelic Sobolev norms | Details will be provided during each class session |
| Class 7 | Ergodic principle | Details will be provided during each class session |
| Class 8 | Subconvex bounds for GL(2)×GL(1) | Details will be provided during each class session |
Study advice (preparation and review)
To enhance effective learning, students are encouraged to spend approximately 100 minutes preparing for class and another 100 minutes reviewing class content afterwards (including assignments) for each class.
They should do so by referring to textbooks and other course material.
Textbook(s)
None required.
Reference books, course materials, etc.
Details will be announced during the course.
Evaluation methods and criteria
Course scores are evaluated by homework assignments (100%). Details will be announced during the course.
Related courses
- MTH.A507 ： Advanced topics in Algebra G1
- MTH.A301 ： Algebra I
- MTH.A302 ： Algebra II
- MTH.C301 ： Complex Analysis I
- MTH.C302 ： Complex Analysis II
Prerequisites
Basic undergraduate algebra and complex analysis