A note on simultaneous diophantine approximation |
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| Authors: | Werner Georg Nowak |
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| Affiliation: | 1. Institut für Mathematik und angewandte Statistik der Universit?t für Bodenkultur, Gregor Mendel-Stra?e 33, A - 1180, Wien, Austria
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| Abstract: | Refining earlier investigations due to J.M.MACK [7] by a method of MORDELL it is proved that for any two irrational numbers α, β there exist infinitely many pairs of fractions p/r, q/r satisfying the inequalities $$|alpha - frac{p}{r}|< frac{8}{{13}}r^{ - 3/2} ,|beta - frac{q}{r}|< frac{8}{{13}}r^{ - 3/2} .$$ . |
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