3 papers
math.NT2009
Characterizing algebraic curves with infinitely many integral points
Yuri Bilu, Alvanos Paraskevas, Poulakis Dimitrios
A classical theorem of Siegel asserts that the set of S-integral points of an algebraic curve C over a number field is finite unless C has genus 0 and at most two points at infinit…
math.NT2008★ 1 cited
Quantitative Riemann existence theorem over a number field
Yuri F. Bilu, Marco Strambi
Given a covering of the projective line with ramifications defined over a number field, we define a plain model of the algebraic curve realizing the Riemann existence theorem for t…
math.NT2008★ 1 cited
Serre's uniformity problem in the split Cartan case
Yuri Bilu, Pierre Parent
We prove that there exists an integer p_0 such that X_split(p)(Q) is made of cusps and CM-points for any prime p>p_0. Equivalently, for any non-CM elliptic curve E over Q and any p…