Acta Mathematica

On the rational approximations to the powers of an algebraic number: Solution of two problems of Mahler and Mendès France

Pietro Corvaja and Umberto Zannier

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Article information

Source
Acta Math., Volume 193, Number 2 (2004), 175-191.

Dates
Received: 13 April 2004
First available in Project Euclid: 31 January 2017

Permanent link to this document
https://projecteuclid.org/euclid.acta/1485891699

Digital Object Identifier
doi:10.1007/BF02392563

Mathematical Reviews number (MathSciNet)
MR2134865

Zentralblatt MATH identifier
1175.11036

Rights
2004 © Institut Mittag-Leffler

Citation

Corvaja, Pietro; Zannier, Umberto. On the rational approximations to the powers of an algebraic number: Solution of two problems of Mahler and Mendès France. Acta Math. 193 (2004), no. 2, 175--191. doi:10.1007/BF02392563. https://projecteuclid.org/euclid.acta/1485891699


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References

  • [CZ] Corvaja, P. & Zannier, U., On the length of the continued fraction for the ratio of two power sums. To appear in J. Théor. Nombres Bordeaux.
  • [Ma] Mahler, K., On the fractional parts of the powers of a rational number, II. Mathematika, 4 (1957), 122–124.
  • [Me] Mendès France, M., Remarks and problems on finite and periodic continued fractions. Enseign. Math., 39 (1993), 249–257.
  • [S] Schmidt, W. M., Diophantine Approximations and Diophantine Equations. Lecture Notes in Math., 1467. Springer, Berlin, 1991.