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

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.

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).

DOI: 10.5802/jtnb.517
Pietro Corvaja 1; Umberto Zannier 2

1 Dipartimento di Matematica Università di Udine via delle Scienze 206 33100 Udine (Italy)
2 Scuola Normale Superiore Piazza dei Cavalieri, 7 56100 Pisa (Italy)
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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, Volume 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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