Simultaneous Diophantine approximation: sums of squares and homogeneous polynomials
Volume 190 / 2019
Acta Arithmetica 190 (2019), 87-100
MSC: Primary 11J13; Secondary 11J54.
DOI: 10.4064/aa180614-18-9
Published online: 7 June 2019
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.
