Hostname: page-component-586b7cd67f-t7czq Total loading time: 0 Render date: 2024-11-29T21:31:14.025Z Has data issue: false hasContentIssue false
  • English
  • Français

Fractional parts of powers of rationals

Published online by Cambridge University Press:  24 October 2008

F. Beukers
F. Beukers
Affiliation:
University of Leiden
Get access Rights & Permissions [Opens in a new window]

Extract

In 1975 A. Baker and J. Coates published a paper bearing the same title (2). Since the introduction to their paper can be used in this paper very appropriately, I shall quote large parts of it here.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 90 , Issue 1 , July 1981 , pp. 13 - 20
Copyright
Copyright © Cambridge Philosophical Society 1981

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Baker, A.Rational approximations to and other algebraic numbers. Quart. J. Math. Oxford 15 (1964), 375–383.CrossRefGoogle Scholar
(2)Baker, A. and Coates, J.Fractional parts of powers of rationals. Math. Proc. Cambridge Philos. Soc. 77 (1975), 269–279.CrossRefGoogle Scholar
(3)Baker, A. and Masser, D. W.Transcendence theory: advances and applications (Academic Press, London, 1977).Google Scholar
(4)Rosser, J. Barkley and Schoenfeld, L.Approximate formulas for some functions of prime numbers. Illinois J. Math. 6 (1962), 64–94.Google Scholar
(5)Beukers, F. The generalised Ramanujan-Nagell equation (Thesis, University of Leiden, Netherlands, to appear in Acta Arithmetica).Google Scholar
(6)Huxley, M. N. and Nair, M.Power free values of polynomials: III. Proc. London Math. Soc. 41 (1980), 66–82.Google Scholar
(7)Mahler, K.On the fractional parts of the powers of a rational number: II. Mathematika 4 (1957), 122–124.CrossRefGoogle Scholar
(8)Siegel, C. L.Die Gleichung axn−byn = c. Math. Ann. 114 (1937), 57–68.Google Scholar