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.
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.
Axiomatic definition of L-functions, analytic properties of L-functions, Weil's explicit formula, Hilbert spaces of entire functions
✔ Specialist skills | Intercultural skills | Communication skills | Critical thinking skills | Practical and/or problem-solving skills |
Standard lecture course.
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 | 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. |
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.
Unspecified.
H. Iwaniec and E. Kowalski, Analytic number theory, Colloquium Publications, 53, AMS
Other course materials are provided during class.
Learning achievement is evaluated by reports (100%).
Basic knowledge of undergraduate algebra and complex analysis