Papers › Refined Selmer equations for the thrice-punctured line in depth two
Refined Selmer equations for the thrice-punctured line in depth two
Alex J. Best, L. Alexander Betts, Theresa Kumpitsch, Martin Lüdtke, Angus W. McAndrew, Lie Qian, Elie Studnia, Yujie Xu
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In [Kim05], Kim gave a new proof of Siegel's Theorem that there are only finitely many S-integral points on ℙ¹_ℤ∖{0,1,∞}. 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 S increases. In this paper, we implement a refinement of Kim's method to explicitly compute various examples where S has size $2$ which has been introduced in [BD19]. In so doing, we exhibit new examples of a natural generalisation of a conjecture of Kim.
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