2023 Faculty Courses School of Science Department of Mathematics Graduate major in Mathematics
Advanced topics in Algebra E1
- 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-112(H117))
- Class
- -
- Course Code
- MTH.A505
- Number of credits
- 100
- Course offered
- 2023
- Offered quarter
- 1Q
- Syllabus updated
- Jul 8, 2025
- Language
- English
Syllabus
Course overview and goals
This course is an introduction to analytic number theory. Particularly, we will study modern tools and concepts in the theory of zeta- and L-functions. This course is followed by Advanced topics in Algebra F1.
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. We begin with the classical Riemann zeta function.
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
Riemann zeta function, functional equation, Prime Number Theorem, zero-free region, explicit formula
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 | Riemann zeta function | Details will be provided during each class session. |
| Class 2 | Analytic continuation and functional equation | Details will be provided during each class session. |
| Class 3 | Special values | Details will be provided during each class session. |
| Class 4 | Partial summation formula | Details will be provided during each class session. |
| Class 5 | Prime Number Theorem | Details will be provided during each class session. |
| Class 6 | Zero-free region | Details will be provided during each class session. |
| Class 7 | Proof of the Prime Number Theorem | 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. Davenport, Multiplicative Number Theory, GTM 74 (3rd revised ed.), New York: Springer-Verlag
H. L. Montgomery and R. C. Vaughan, Multiplicative Number Theory I : Classical Theory, CSAM 97. Cambridge University Press
Ohter 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.A506 ： Advanced topics in Algebra F1
Prerequisites
Basic knowledge of undergraduate algebra and complex analysis