Aurélien Bajolet

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Présentation

Je suis actuellement en Thèse à l'université Bordeaux 1 sous la direction de Yu. Bilu . Mes travaux portent sur la résolution effective de problèmes diophantiens telles que la résolution d'équations diophantiennes ou la recherche de points entiers sur les courbes modulaires. Vous trouverez sur cette page mon CV ainsi que mes articles.

Articles

Articles publiés

On the Diophantine equation x4+q4=p yr with B. Dupuy, F. Luca and A. Togbe Publicationes Mathematicae Debrecen 79 / 3-4 (2) (2011) . [Preprint].

Abstract. In this paper, we characterize up to finitely many exceptions all the solutions of the Diophantine equation x4+q4=p yr with r > 3 a fixed prime. When r = 5, we show that there are no exceptions.

Bouding j-invariant of integral points on Xns+(p) with M. Sha (2012). À paraître dans Proceedings of the American Mathematical Society [ Preprint ] .

Abstract. For prime p ≥ 7, by using Baker’s method we obtain two explicit bounds in terms of p for the j-invariant of an integral point on Xns+(p) which is the modular curve of level p corresponding to the normalizer of a non-split Cartan subgroup of GL2(Z/pZ).

Articles en prépration

Computing Integral Points on Xns+(p) with Yu. Bilu. [ Preprint ] .

Abstract. We describe an algorithm for computing integral points on the modular curve of prime level p associated to the normalizer of a non-split Cartan subgroup of GL2(Fp). Using our method, we show that for 7 < p < 71 the only integral points on this curve are the CM-points.