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Simultaneous Diophantine approximation: sums of squares and homogeneous polynomials

Volume 190 / 2019

Dmitry Kleinbock, Nikolay Moshchevitin Acta Arithmetica 190 (2019), 87-100 MSC: Primary 11J13; Secondary 11J54. DOI: 10.4064/aa180614-18-9 Published online: 7 June 2019


Let $f$ be a homogeneous polynomial with rational coefficients in $d$ variables. We prove several results concerning uniform simultaneous approximation to points on the graph of $f$, as well as on the hypersurface $\{f(x_1,\dots,x_d) = 1\}$. The results are first stated for the case $f(x_1,\dots,x_d) = x_1^2+\dots+x_d^2,$ which is of particular interest.


  • Dmitry KleinbockBrandeis University
    Waltham, MA 02454-9110, U.S.A.
  • Nikolay MoshchevitinMoscow State University
    Leninskie Gory 1
    Moscow, Russia, 119991
    Astrakhan State University
    Tatishcheva 20a
    Astrakhan, Russia, 414056

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