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A note on simultaneous diophantine approximation

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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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References

  1. CASSELS, J.W.S.: Simultaneous diophantine approximation. J.London Math.Soc.30, 119–121(1955)

    Google Scholar 

  2. CASSELS, J.W.S.: An introduction to the geometry of numbers. Berlin-Göttingen-Heidelberg: Springer 1959

    Google Scholar 

  3. DAVENPORT, H.: Simultaneous diophantine approximation. Proc. London Math. Soc. (3)2, 406–416 (1952)

    Google Scholar 

  4. DAVENPORT, H.: On a theorem of Furtwängler. J.London Math.Soc.30, 186–195 (1955)

    Google Scholar 

  5. DAVENPORT, H.: Mahler, K.: Simultaneous diophantine approximation. Duke Math.J.13, 105–111 (1946)

    Google Scholar 

  6. MACK, J.M.: Simultaneous diophantine approximation. Ph.D. thesis, University of Sydney 1971

  7. MACK, J.M.: Simultaneous diophantine approximation. J.Austral. Math.Soc.24 (Series A), 266–285 (1977)

    Google Scholar 

  8. MULLENDER, P.: Simultaneous approximation. Annals of Mathematics52, 417–426 (1950)

    Google Scholar 

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Authors and Affiliations

  1. Institut für Mathematik und angewandte Statistik der Universität für Bodenkultur, Gregor Mendel-Straße 33, A - 1180, Wien, Austria

    Werner Georg Nowak

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  1. Werner Georg Nowak
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Nowak, W.G. A note on simultaneous diophantine approximation. Manuscripta Math 36, 33–46 (1981). https://doi.org/10.1007/BF01174811

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  • DOI: https://doi.org/10.1007/BF01174811

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