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Roth’s Theorem

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Part of the Lecture Notes in Mathematics book series (LNM,volume 785)

Abstract

THEOREM 1A (Liouville (1844)). Suppose α is a real algebraic number of degree d. Then there is a constant c(α) > 0 such that

$$ \left| {\alpha - \frac{p} {q}} \right| > \frac{{c(\alpha )}} {{q^d }} $$

for every rational \( \tfrac{p} {q} \) distinct from α.

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References

  • A. Thue (1908). Om en generel i store hele taluløsbar ligning. Kra. Vidensk. Selsk. Skrifter. I. Mat. Nat. Kl. No. 7. Kra.

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© 1980 Springer-Verlag Berlin Heidelberg

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(1980). Roth’s Theorem. In: Diophantine Approximation. Lecture Notes in Mathematics, vol 785. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-38645-2_5

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  • DOI: https://doi.org/10.1007/978-3-540-38645-2_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-09762-4

  • Online ISBN: 978-3-540-38645-2

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