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arXiv · 1108.4435

Positive integers: counterexample to W.M. Schmidt's conjecture

Nikolay G. Moshchevitin
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Abstract

We show that there exist real numbers $α_1,α_2$ linearly independent over $\mathbb{Z}$ together with 1 such that for every non-zero integer vector $(m_1,m_2)$ with $m_1\ge 0$ and $m_2\ge 0$ one has $||m_1α_1+m_2α_2|| \ge 2^{-300} (\max(m_1, m_2))^{-σ}$ with $σ= 1.94696^+$.

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Nikolay G. Moshchevitin. 2011-08-22. Positive integers: counterexample to W.M. Schmidt's conjecture. https://arxiv.org/abs/1108.4435

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