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The generalization of Jarník’s identity

Volume 175 / 2016

Wolfgang M. Schmidt, Leonhard Summerer Acta Arithmetica 175 (2016), 119-136 MSC: 11H06, 11J13. DOI: 10.4064/aa8316-5-2016 Published online: 15 September 2016


We will give a new proof, using the Parametric Geometry of Numbers, for remarkable inequalities of O. German which generalize the classical Jarník identity on simultaneous approximation. We will also show that these inequalities are best possible.


  • Wolfgang M. SchmidtDepartment of Mathematics
    University of Colorado
    Boulder, CO 80309-0395, U.S.A.
  • Leonhard SummererFakultät für Mathematik der Universität Wien
    Oskar-Morgenstern-Platz 1
    1090 Wien, Austria

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