Positive integers: counterexample to W.M. Schmidt's conjecture
Moshchevitin, Nikolay G.
Original · EN
We show that there exist real numbers α₁,α₂ linearly independent over Z together with 1 such that for every non-zero integer vector (m₁,m₂) with m₁≥ 0 and m₂≥ 0 one has ||m₁α₁+m₂α₂|| ≥ 2⁻³⁰⁰ ((m₁, m₂))⁻σ with σ= 1.94696+.
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