A Khintchine type theorem for hyperplanes

We prove that the convergence Khintchine theorem holds for affine hyperplanes whose parametrizing matrices satisfy a mild Diophantine condition. We use the dynamical method of Kleinbock-Margulis.Comment: 14 page

Diophantine approximation on lines with prime constraints

We study the problem of Diophantine approximation on lines in R^2 with prime numerator and denominator.Comment: 14 page

Remarks on Diophantine approximation in function fields

We study some problems in metric Diophantine approximation over local fields of positive characteristic.Comment: To appear in Mathematica Scandinavic

Restricted simultaneous Diophantine approximation

We study the problem of Diophantine approximation on lines in $\mathbb{R}^d$ under certain primality restrictions.Comment: 16 pages. arXiv admin note: text overlap with arXiv:1309.529