• Corpus ID: 235485159

Refined Selmer equations for the thrice-punctured line in depth two

  title={Refined Selmer equations for the thrice-punctured line in depth two},
  author={Alex J Best and L. Alexander Betts and Theresa Kumpitsch and Martin Ludtke and Angus McAndrew and Li Qian and Elie Studnia and Yujie Xu},
In [Kim05], Kim gave a new proof of Siegel’s Theorem that there are only finitely many S-integral points on PZ \ {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… 
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