In a recent paper we proved that there are at most finitely many complex numbers such that the points and are both torsion on the Legendre elliptic curve defined by . In a sequel we gave a generalization to any two points with coordinates algebraic over the field and even over . Here we reconsider the special case and with complex numbers and .
Nous avons déjà démontré qu’il n’existe qu’un nombre fini de nombres complexes tels que les points et soient d’ordre fini sur la courbe elliptique de Legendre définie par . Nous avons généralisé ensuite ce résultat aux couples de points algébriques quelconques sur . Nous revenons ici aux points et avec des nombres complexes et quelconques.
@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/} }
TY - JOUR TI - Bicyclotomic polynomials and impossible intersections JO - Journal de Théorie des Nombres de Bordeaux PY - 2013 DA - 2013/// SP - 635 EP - 659 VL - 25 IS - 3 PB - Société Arithmétique de Bordeaux UR - https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.851/ UR - https://zbmath.org/?q=an%3A06291370 UR - https://www.ams.org/mathscinet-getitem?mr=3179679 UR - https://doi.org/10.5802/jtnb.851 DO - 10.5802/jtnb.851 LA - en ID - JTNB_2013__25_3_635_0 ER -
David Masser; Umberto Zannier. Bicyclotomic polynomials and impossible intersections. Journal de Théorie des Nombres de Bordeaux, Volume 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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