Introduction to complex L-functions and the Deligne conjecture
Student No.:50
Time:Mon/Fri 8:00-9:35, 2017-07-03~2017-07-28
Instructor:Jie Lin  [IHES]
Place:Conference Room 3, Floor 2, Jin Chun Yuan West Building
Starting Date:2017-7-3
Ending Date:2017-7-28
The goal of this mini-course is to introduce the Deligne conjecture on critical values of L-functions. We will start from special values of Dirichlet L-functions. Then we will introduce the Langlands program and some other L-functions. We will explain the Deligne conjecture afterwards. If time permits, we will show that this conjecture is compatible with some other conjectures on special values such as the BSD conjecture, the Ichino-Ikeda conjecture etc.
This course will contain some theoretic explanation as well as some concreteexamples. The contents may vary according to the level of the audience.
Complex analysis and linear algebra. Some basics in algebraic number theory and algebraic topology will be helpful but not obligatory. At least two-thirds of the contents are accessible to second-year undergraduate students.
[1] J. Bernstein and S.Gelbart (eds.), “An introduction to the Langlands
 program”, Birkhauser Bonston, 2004.
[2] P. Deligne, “Valeurs de fonctions L et périodes d’intégrales”, in “Automorphic forms, representations and L-functions” (A. Borel and W. Casselman, eds.), Proceedings of the Symposium in Pure Mathematics, vol. 33, American Mathematical Society, 1979.
[3] M. Harris, “L-functions and periods of adjoint motives”, Algebra and Number Theory (2013), no. 7, 117--155.