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Siegel's lemma, Padé approximations and jacobians

Enrico Bombieri, Paula B. Cohen (1997)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Siegel’s theorem and the Shafarevich conjecture

Aaron Levin (2012)

Journal de Théorie des Nombres de Bordeaux

It is known that in the case of hyperelliptic curves the Shafarevich conjecture can be made effective, i.e., for any number field $k$ and any finite set of places $S$ of $k$ , one can effectively compute the set of isomorphism classes of hyperelliptic curves over $k$ with good reduction outside $S$ . We show here that an extension of this result to an effective Shafarevich conjecture for Jacobians of hyperelliptic curves of genus $g$ would imply an effective version of Siegel’s theorem for integral points on...

Some diophantine equations of the form $x^{n} + y^{n} = z^{m}$

Bjorn Poonen (1998)

Acta Arithmetica

Some special curves of genus 5

Andrew Bremner (1997)