Best, Alex J.

Betts, L. Alexander

Kumpitsch, Theresa

Lüdtke, Martin

McAndrew, Angus W.

Qian, Lie

Studnia, Elie

Xu, Yujie

English

In [Kim05], Kim gave a new proof of Siegel's Theorem that there are only finitely many $S$-integral points on $\mathbb P^1_{\mathbb Z}\setminus\{0,1,\infty\}$. 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

ARTS repository - University of Groningen

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

https://pure.rug.nl/ws/files/249097628/2106.10145v1.pdf

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

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ARTS repository - University of Groningen