2023 Faculty Courses School of Science Department of Mathematics Graduate major in Mathematics
Advanced topics in Algebra F1
- Academic unit or major
- Graduate major in Mathematics
- Instructor(s)
- Masatoshi Suzuki
- Class Format
- Lecture (Face-to-face)
- Media-enhanced courses
- -
- Day of week/Period
(Classrooms) - 5-6 Mon (M-143B(H119B))
- Class
- -
- Course Code
- MTH.A506
- Number of credits
- 100
- Course offered
- 2023
- Offered quarter
- 2Q
- Syllabus updated
- Jul 8, 2025
- Language
- English
Syllabus
Course overview and goals
This course follows Advanced topics in Algebra E1.
Zeta- and L-functions appear in many areas of number theory, and are studied very actively. This course hopes to provide solid background for students intending to learn advanced topics on zeta- and L-functions. Based on Advanced topics in Algebra E1, we study analytic properties of more general L-functions defined axiomatically.
Course description and aims
Students are expected to:
-- understand fundamental notions and methods of analytic number theory
-- be familiar with modern tools and concepts in the theory of zeta- and L-functions.
Keywords
Axiomatic definition of L-functions, analytic properties of L-functions, Weil's explicit formula, Hilbert spaces of entire functions
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 | Axiomatic definition of L-functions | Details will be provided during each class session. |
| Class 2 | Analytic properties of L-functions | Details will be provided during each class session. |
| Class 3 | subconvexity problem | Details will be provided during each class session. |
| Class 4 | Generalized Riemann hypothesis | Details will be provided during each class session. |
| Class 5 | Weil's explicit formula | Details will be provided during each class session. |
| Class 6 | Hermite-Biehler class | Details will be provided during each class session. |
| Class 7 | Hilbert spaces of entire functions | 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)
Unspecified.
Reference books, course materials, etc.
H. Iwaniec and E. Kowalski, Analytic number theory, Colloquium Publications, 53, AMS
Other course materials are provided during class.
Evaluation methods and criteria
Learning achievement is evaluated by reports (100%).
Related courses
- MTH.A301 ： Algebra I
- MTH.A302 ： Algebra II
- MTH.A331 ： Algebra III
- MTH.A505 ： Advanced topics in Algebra E1
Prerequisites
Basic knowledge of undergraduate algebra and complex analysis