Bicyclotomic polynomials and impossible intersections
Journal de théorie des nombres de Bordeaux, Tome 25 (2013) no. 3, pp. 635-659.

Nous avons déjà démontré qu’il n’existe qu’un nombre fini de nombres complexes t0,1 tels que les points (2,2(2-t)) et (3,6(3-t)) soient d’ordre fini sur la courbe elliptique de Legendre définie par y 2 =x(x-1)(x-t). Nous avons généralisé ensuite ce résultat aux couples de points algébriques quelconques sur C(t). Nous revenons ici aux points (u,u(u-1)(u-t)) et (v,v(v-1)(v-t)) avec des nombres complexes u et v quelconques.

In a recent paper we proved that there are at most finitely many complex numbers t0,1 such that the points (2,2(2-t)) and (3,6(3-t)) are both torsion on the Legendre elliptic curve defined by y 2 =x(x-1)(x-t). In a sequel we gave a generalization to any two points with coordinates algebraic over the field Q(t) and even over C(t). Here we reconsider the special case (u,u(u-1)(u-t)) and (v,v(v-1)(v-t)) with complex numbers u and v.

DOI : 10.5802/jtnb.851
Classification : 11G05, 14H52
Masser, David 1 ; Zannier, Umberto 2

1 Mathematisches Institut Universität Basel, Rheinsprung 21 4051 Basel, Switzerland
2 Scuola Normale, Piazza Cavalieri 7 56126 Pisa, Italy
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Masser, David; Zannier, Umberto. Bicyclotomic polynomials and impossible intersections. Journal de théorie des nombres de Bordeaux, Tome 25 (2013) no. 3, pp. 635-659. doi : 10.5802/jtnb.851. http://www.numdam.org/articles/10.5802/jtnb.851/

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