The method of Thue-Siegel for binary quartic forms
The number of solutions of linear equations in roots of unity
The resolution of the diophantine equation x(x+d)...(x+(k-1)d) = by² for fixed d
The simultaneous Pell equations y²-Dz² = 1 and x²-2Dz² = 1
Théorème d'irréductibilité de Hilbert effectif
Trivial points on towers of curves
In order to study the behavior of the points in a tower of curves, we introduce and study trivial points on towers of curves, and we discuss their finiteness over number fields. We relate the problem of proving that the only rational points are the trivial ones at some level of the tower, to the unboundeness of the gonality of the curves in the tower, which we show under some hypothesis.
Über die Anzahl der Lösungen gewisser diophantischer Gleichungen dritten Grades
Unbounded discrepancy in Frobenius numbers.
Uniformly counting rational points on conics
We provide an asymptotic estimate for the number of rational points of bounded height on a non-singular conic over ℚ. The estimate is uniform in the coefficients of the underlying quadratic form.
Yet another generalization of the Ramanujan-Nagell equation
Линейные формы от значений G-функций и диофантовы уравнения