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- Academic unit or major
- Mathematics
- Instructor(s)
- Suzuki Masatoshi
- Class Format
- Lecture
- Media-enhanced courses
- Day/Period(Room No.)
- Thr5-6(H137)
- Group
- -
- Course number
- ZUA.A333
- Credits
- 1
- Academic year
- 2019
- Offered quarter
- 3Q
- Syllabus updated
- 2019/3/18
- Lecture notes updated
- -
- Language used
- English
- Access Index
-
Course description and aims
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 D.
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.
Student learning outcomes
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 that will be developed
| ✔ 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 assignments.
Course schedule/Required learning
| Course schedule | Required learning | |
|---|---|---|
| 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 |
| Class 8 | Explicit formula | Details will be provided during each class session |
Textbook(s)
None required
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
Assessment criteria and methods
Course scores are evaluated by homework assignments (100%). Details will be announced during the course.
Related courses
- MTH.A407 ： Advanced topics in Algebra C1
- MTH.A408 ： Advanced topics in Algebra D1
- ZUA.A334 ： Advanced courses in Algebra D
Prerequisites (i.e., required knowledge, skills, courses, etc.)
Basic undergraduate algebra and complex analysis
Other
None in particular.
