Rational points of elliptic curves and derivatives of their zeta functions


天數 202


2020-03-30 (星期一) 14:10 - 15:00


Given an elliptic curve E over the rational number field, the Birch and Swinnerton-Dyer conjecture suggests that there be infinitely rational points in E whenever the associated Hasse-Weil zeta function vanishes at s=1, but it is not clear how one can construct these rational points from this complex zeta function. However, if we consider the p-adic counterparts of the complex zeta function of E, then in some favorable cases, one can actually recover rational points from values (or derivatives) of these p-adic zeta functions. In this talk, we plan to explain some examples along this direction.


15:00 - 15:30