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A diophantine problem in harmonic analysis

Published online by Cambridge University Press:  24 October 2008

A. J. Van Der Poorten  and
H. P. Schlickewei
A. J. Van Der Poorten
Affiliation:
School of MPCE, Macquarie University, NSW 2109, Australia
H. P. Schlickewei
Affiliation:
Abteilung für Mathematik, Oberer Eselsberg, Universität Ulm, D 7900 Ulm, Germany
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Extract

In the problem session of the Journées Arithmétiques 1989 in Luminy, Bourgain made the following

Conjecture. Suppose α is an algebraic number of degree d. Assume that for each n∈ ℕ

Then there exists a constant c = c(α) with the following property: given any subspace W of dimension ≤ d − 1 of the d-dimensional ℚ-vector space ℚ(α), the set {n|n∈ℕ,αn∈W} contains fewer than c(α) elements.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 108 , Issue 3 , November 1990 , pp. 417 - 420
Copyright
Copyright © Cambridge Philosophical Society 1990

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References

REFERENCES

[1]Bourgain, J.. The Riesz–Raikov Theorem for algebraic numbers. (To appear.)Google Scholar
[2]Schlickewei, H. P.. The quantitative Subspace Theorem for number fields. (To appear.)Google Scholar
[3]Scklickewei, H. P.. S-unit equations over number fields. Invent. Math. (To appear.)Google Scholar
[4]Schmidt, W. M.. The Subspace Theorem in diophantine approximations. Compositio Math. 69 (1989), 121–173.Google Scholar