2020 Faculty Courses School of Science Department of Mathematics Graduate major in Mathematics
Advanced topics in Algebra F
- Academic unit or major
- Graduate major in Mathematics
- Instructor(s)
- Masatoshi Suzuki
- Class Format
- Lecture (Zoom)
- Media-enhanced courses
- -
- Day of week/Period
(Classrooms) - Intensive (Zoom)
- Class
- -
- Course Code
- MTH.A502
- Number of credits
- 100
- Course offered
- 2020
- 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 E.
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
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 representation of GL(n) | Details will be provided during each class session |
| Class 2 | Adelization of classical automorphic forms | Details will be provided during each class session |
| Class 3 | Eisenstein series | Details will be provided during each class session |
| Class 4 | Revisit the subconvexity problem | Details will be provided during each class session |
| Class 5 | The Burgess bound | Details will be provided during each class session |
| Class 6 | Integral representations of L-functions (1) | Details will be provided during each class session |
| Class 7 | Integral representations of L-functions (2) | Details will be provided during each class session |
| Class 8 | Subconvex bounds for Rankin-Selberg L-functions | Details will be provided during each class session |
Study advice (preparation and review)
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.A501 ： Advanced topics in Algebra E
- 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