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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.A334
- Credits
- 1
- Academic year
- 2019
- Offered quarter
- 4Q
- Syllabus updated
- 2019/3/18
- Lecture notes updated
- -
- Language used
- English
- Access Index
-
Course description and aims
This course follows Advanced topics in Algebra C.
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 C, we study more general L-functions defined axiomatically.
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
Axiomatic definition of L-functions, analytic properties of L-functions, Selberg trace formula, Weil's 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 | 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 | Generalized Riemann hypothesis and other conjecturtes | Details will be provided during each class session |
| Class 4 | Selberg trace formula | Details will be provided during each class session |
| Class 5 | Selberg zeta functions | Details will be provided during each class session |
| Class 6 | Weil's explicit formula | Details will be provided during each class session |
| Class 7 | Spectral interpretation of zeros I | Details will be provided during each class session |
| Class 8 | Spectral interpretation of zeros II | Details will be provided during each class session |
Textbook(s)
None required
Reference books, course materials, etc.
H. Iwaniec and E. Kowalski, Analytic number theory, Colloquium Publications, 53, AMS
H. Iwaniec and P. Sarnak, Perspectives on the analytic theory of L-functions, Geom. Funct. Anal. 2000, 705-741
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.A333 ： Advanced courses in Algebra C
Prerequisites (i.e., required knowledge, skills, courses, etc.)
Basic undergraduate algebra and complex analysis
Other
None in particular.
