S.-T. Yau High School Science Awarded Papersmathscidoc:1801.35002
Yau Science Award (Math), 2017.12
We reduced the unsolved problem of Evans triangles to
the problem of nding rational points on a class of elliptic curves,
the twisted Edwards curves En. We proved that the set of all Evans
triangles with a given ratio is isomorphic to a quotient group of En(Q).
After this, using Sage, we can solve the Evans problem for an amount
of cases within the capacity of computer. Even without the help of
a computer, we can still obtain a large class of new Evans triangles,
and nd an e ective way to test if the rank of an Edwards curve is
positive or not.
@inproceedings{wensen2017evans,
title={Evans Triangles and Edwards Curves},
author={Wensen Wu},
url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20180113194414598184875},
booktitle={Yau Science Award (Math)},
year={2017},
}
Wensen Wu. Evans Triangles and Edwards Curves. 2017. In Yau Science Award (Math). http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20180113194414598184875.