Solutions entières de l’équation Y m =f(X)
Journal de Théorie des Nombres de Bordeaux, Tome 3 (1991) no. 1, pp. 187-199.

Soit K un corps de nombres. Dans ce travail nous calculons des majorants effectifs pour la taille des solutions en entiers algébriques de K des équations, Y 2 =f(X), où f(X)K[X] a au moins trois racines d’ordre impair, et Y m =f(X)m3 et f(X)K[X] a au moins deux racines d’ordre premier à m. On améliore ainsi les estimations connues ([2],[9]) pour les solutions de ces équations en entiers algébriques de K.

Let K be a number field. In this work we give effective upper bounds for the size of solutions in algebraic integers of K, of equations Y 2 =f(X), where f(X)K[X] has at least three roots of odd order, and Y m =f(X) where f(X)K[X] has at least two roots of order prime to m. We thus improve the known estimations ([2],[9]) for the solutions of these equations in algebraic integers of K.

@article{JTNB_1991__3_1_187_0,
     author = {Poulakis, Dimitrios},
     title = {Solutions enti\`eres de l{\textquoteright}\'equation $Y^m = f(X)$},
     journal = {Journal de Th\'eorie des Nombres de Bordeaux},
     pages = {187--199},
     publisher = {Universit\'e Bordeaux I},
     volume = {3},
     number = {1},
     year = {1991},
     doi = {10.5802/jtnb.47},
     zbl = {0733.11009},
     mrnumber = {1116106},
     language = {fr},
     url = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.47/}
}
Dimitrios Poulakis. Solutions entières de l’équation $Y^m = f(X)$. Journal de Théorie des Nombres de Bordeaux, Tome 3 (1991) no. 1, pp. 187-199. doi : 10.5802/jtnb.47. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.47/

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