Simon Kristensen

On shrinking targets for Zm actions on tori

Let A be an n by m matrix with real entries. Consider the set Bad_A of x \in [0,1)^n for which there exists a constant c(x)>0 such that for any q \in Z^m the distance between x and the point {Aq} is at least c(x) |q|^{-m/n}. It is shown that the intersection of Bad_A with any suitably regular fractal set is of maximal Hausdorff dimension. The linear form systems investigated in this paper are natural extensions of irrational rotations of the circle. Even in the latter one-dimensional case, the results obtained are new.

METRICAL RESULTS ON SYSTEMS OF SMALL LINEAR FORMS

In this paper the metric theory of Diophantine approximation associated with the small linear forms is investigated. Khintchine–Groshev theorems are established along with Hausdorff measure generalization without the monotonic assumption on the approximation function.

A quantitative Khintchine-Groshev type theorem over a field of formal series

Abstract An asymptotic formula which holds almost everywhere is obtained for the number of solutions to theDiophantine inequalities ‖qA − p‖ 1) over the field of formal Laurent series with coefficients from a finite field, and p and q are vectors of polynomials over the same finite field.

Diophantine exponents for mildly restricted approximation

We are studying the Diophantine exponent μn,l defined for integers 1≤l<n and a vector α∈ℝn by letting

KHINTCHINE'S THEOREM AND TRANSFERENCE PRINCIPLE FOR STAR BODIES

\mu_{n,l}=\sup\{\mu\geq0: 0 < \Vert\underline{x}\cdot\alpha\Vert<H(\underline{x})^{-\mu}\ \text{for infinitely many}\ \underline{x}\in\mathcal{C}_{n,l}\cap\mathbb{Z}^n\},

Carbon dioxide and methane emissions from the scale model of open dairy lots

where

Novel regression methods for metacognition

\cdot

A problem in non-linear Diophantine approximation.

is the scalar product,