On the length of the continued fraction for values of quotients of power sums
Journal de Théorie des Nombres de Bordeaux, Tome 17 (2005) no. 3, pp. 737-748.

En généralisant un résultat de Pourchet, nous démontrons que si α,β sont deux sommes de puissances définies sur , satisfaisant certaines conditions nécessaires, la longueur de la fraction continue pour α(n)/β(n) tend vers l’infini pour n. On déduira ce résultat d’une inégalité de type Thue uniforme pour les approximations rationnelles des nombres de la forme α(n)/β(n).

Generalizing a result of Pourchet, we show that, if α,β are power sums over satisfying suitable necessary assumptions, the length of the continued fraction for α(n)/β(n) tends to infinity as n. This will be derived from a uniform Thue-type inequality for the rational approximations to the rational numbers α(n)/β(n), n.

@article{JTNB_2005__17_3_737_0,
     author = {Pietro Corvaja and Umberto Zannier},
     title = {On the length of the continued fraction for values of quotients of power sums},
     journal = {Journal de Th\'eorie des Nombres de Bordeaux},
     pages = {737--748},
     publisher = {Universit\'e Bordeaux 1},
     volume = {17},
     number = {3},
     year = {2005},
     doi = {10.5802/jtnb.517},
     zbl = {05016584},
     mrnumber = {2212122},
     language = {en},
     url = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.517/}
}
Pietro Corvaja; Umberto Zannier. On the length of the continued fraction for values of quotients of power sums. Journal de Théorie des Nombres de Bordeaux, Tome 17 (2005) no. 3, pp. 737-748. doi : 10.5802/jtnb.517. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.517/

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