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A diophantine problem in harmonic analysis
Published online by Cambridge University Press: 24 October 2008
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
References
REFERENCES
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[4]Schmidt, W. M.. The Subspace Theorem in diophantine approximations. Compositio Math. 69 (1989), 121–173.Google Scholar