Научный комитет: Федор Богомолов (Courant Institute, НИУ ВШЭ), Михаил Вербицкий (НИУ ВШЭ), Алексей Зыкин (НИУ ВШЭ, ИППИ РАН, Лаборатория Понселе).
Zeta functions coming from geometry
Marc Hindry (Université Paris VII, Франция; Laboratoire CNRS J.-V. Poncelet, Москва)
Видеозаписи лекций
Резюме
We plan to give an overview of one of the most beautiful and fruitful
tool for local-global problems in arithmetic geometry : zeta functions.
- Classical zeta functions :
Riemann zeta function, Dirichlet L-functions,
prime number theorem and arithmetic progression theorem;
Dedekind zeta functions and Artin L-functions,
Chebotarev theorem.
- Zeta functions from algebraic geometry :
Weil zeta function (for a variety over a finite field);
Hasse-Weil L-functions (for a variety over a number field);
L-function associated to a Galois representation or a modular form.
- Analytic theory of zeta functionsc:
Analytic continuation and functional equations;
Analytic estimates;
Generalized Riemann hypothesis.
- Special values of zeta functions:
Class number formula;
Birch and Swinnerton Dyer conjecture;
Brauer-Siegel type theorems.
If time permits, we will mention other conjectures on special values : Deligne, Beilinson, etc.
The list of references