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- Liberal arts and basic science courses
- Academic unit or major
- Graduate major in Mathematics
- Instructor(s)
- Suzuki Masatoshi
- Class Format
- Lecture
- Media-enhanced courses
- Day/Period(Room No.)
- Thr5-6(H137)
- Group
- -
- Course number
- MTH.A408
- Credits
- 1
- Academic year
- 2017
- Offered quarter
- 4Q
- Syllabus updated
- 2017/3/17
- Lecture notes updated
- -
- Language used
- Japanese
- Access Index
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Course description and aims
This course follows Advanced topics in Algebra C1.
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 C1, 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
general L-functions, approximate functional equations, convexity bounds, zero-free regions, generalized Riemann hypothesis
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 | Arithmetic functions | Details will be provided during each class |
| Class 2 | Axiomatic definition of L-functions | Details will be provided during each class |
| Class 3 | Analytic conductor, Ramanujan–Petersson conjecture | Details will be provided during each class |
| Class 4 | Approximate functional equations | Details will be provided during each class |
| Class 5 | Convexity bounds of L-functions | Details will be provided during each class |
| Class 6 | Zero-free regions of L-functions | Details will be provided during each class |
| Class 7 | Generalized prime number theorem, Weil's explicit formula | Details will be provided during each class |
| Class 8 | Number theoretic consequences of the generalized Riemann hypothesis | Details will be provided during each class |
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
Assignments (100%).
Related courses
- MTH.A407 ： Advanced topics in Algebra C1
Prerequisites (i.e., required knowledge, skills, courses, etc.)
None required.
Other
None in particular.
