accepted for publication

}, pages = {15-33}, abstract = {After defining a notion of epsilon-density, we provide for any integer m\>1 and real algebraic number alpha an estimate of the smallest epsilon such that the set of vectors of the form (t,t^alpha,...,t alpha^{m-1}) for tR is epsilon-dense modulo 1 in terms of the multiplicative Mahler measure M(A(x)) of the minimal integral polynomial A(x) of alpha, which is independent of m. In particular, we show that if alpha has degree d it is possible to take epsilon = 2^{[d/2]}/M(A(x)). On the other side we show using asymptotic estimates for Toeplitz determinants that we cannot have epsilon$-density for sufficiently large m whenever epsilon is strictly smaller than 1/M(A(x)). In the process of proving this we obtain a result of independent interest about the structure of the Z-module of integral linear recurrences of fixed length determined by a non-monic polynomial.

}, keywords = {Robotics}, issn = {0065-1036}, doi = {10.4064/aa153-1-2}, url = {http://journals.impan.pl/cgi-bin/doi?aa153-1-2}, author = {N. Dubbini and M. Monge} }