Elliptic curves over function fields and special values of L-functions.
Abstract:
From the works of Weil, Jacquet-Langlands, and Deligne, the Hasse-Weil L-functions of elliptic curves over function fields always come from automorphic cusp forms on GL(2) In this talk, I will discuss the recent knowledge on the conjecture of Birch and Swinnerton-Dyer conjecture for
elliptic curves over function fields, and show my current works on the central critical values of L-functions. By Tate's result (1995), this gives a way to determine the finiteness of the Mordell-Weil group of the elliptic curve in question.
Tea Time: 3:30PM R707(七樓休息室)