Simultaneous Diophantine approximation: sums of squares and homogeneous polynomials

Dmitry Kleinbock; Nikolay Moshchevitin

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arXiv · 1803.09306

Simultaneous Diophantine approximation: sums of squares and homogeneous polynomials

Dmitry Kleinbock·Nikolay Moshchevitin

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Abstract

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.

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Dmitry Kleinbock, Nikolay Moshchevitin. 2018-03-25. Simultaneous Diophantine approximation: sums of squares and homogeneous polynomials. https://arxiv.org/abs/1803.09306

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