Simultaneous Diophantine approximation: sums of squares and homogeneous polynomials

Dmitry Kleinbock; Nikolay Moshchevitin

Simultaneous Diophantine approximation: sums of squares and homogeneous polynomials

Number Theory 2018-09-20 v4 Dynamical Systems

Authors: Dmitry Kleinbock , Nikolay Moshchevitin

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.

Keywords

simultaneous Diophantine approximation homogeneous polynomials sums of squares uniform approximation hypersurface

Cite

@article{arxiv.1803.09306,
  title  = {Simultaneous Diophantine approximation: sums of squares and homogeneous polynomials},
  author = {Dmitry Kleinbock and Nikolay Moshchevitin},
  journal= {arXiv preprint arXiv:1803.09306},
  year   = {2018}
}

Comments

18 pages; minor corrections and reformatting

Simultaneous Diophantine approximation: sums of squares and homogeneous polynomials

Abstract

Keywords

Cite

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