8 citations · 9 across the 2 of their papers we have counts for
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math.NT2011★ 8 cited
Rational points on X_0^+ (p^r)
Yu. Bilu, P. Parent, M. Rebolledo
We show how the recent isogeny bounds due to É. Gaudron and G. Rémond allow to obtain the triviality of X_0^+ (p^r)(Q), for r>1 and p a prime exceeding 2.10^{11}. This includes the…
math.NT2009
Runge's Method and Modular Curves
Yuri Bilu, Pierre Parent
We bound the j-invariant of S-integral points on arbitrary modular curves over arbitrary fields, in terms of the congruence group defining the curve, assuming a certain Runge condi…
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…