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.

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DOI : https://doi.org/10.5802/jtnb.851
Classification : 11G05,  14H52
@article{JTNB_2013__25_3_635_0,
     author = {David Masser and Umberto Zannier},
     title = {Bicyclotomic polynomials and impossible intersections},
     journal = {Journal de Th\'eorie des Nombres de Bordeaux},
     pages = {635--659},
     publisher = {Soci\'et\'e Arithm\'etique de Bordeaux},
     volume = {25},
     number = {3},
     year = {2013},
     doi = {10.5802/jtnb.851},
     zbl = {06291370},
     mrnumber = {3179679},
     language = {en},
     url = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.851/}
}
David Masser; Umberto Zannier. 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. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.851/

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