7 research outputs found
Refined Selmer equations for the thrice-punctured line in depth two
In [Kim05], Kim gave a new proof of Siegel's Theorem that there are only
finitely many -integral points on . One advantage of Kim's method is that it in
principle allows one to actually find these points, but the calculations grow
vastly more complicated as the size of increases. In this paper, we
implement a refinement of Kim's method to explicitly compute various examples
where has size which has been introduced in [BD19]. In so doing, we
exhibit new examples of a natural generalisation of a conjecture of Kim.Comment: 58 pages, comments welcom