Metrical Diophantine approximation for quaternions

Metrical Diophantine Approximation for Continued Fraction like Maps of the Interval

We study the metrical properties of a class of continued fractionlike mappings of the unit interval, each of which is defined as the fractional part of a Möbius transformation taking the endpoints of the interval to zero and infinity.

Metrical Theorems for Inhomogeneous Diophantine Approximation in Positive Characteristic

We consider inhomogeneous Diophantine approximation for formal Laurent series over a finite base field. We establish an analogue of a strong law of large numbers due to W. M. Schmidt with a better error term than in the real case. A special case of our result improves upon a recent result by H. Nakada and R. Natsui and completes a result of M. M. Dodson, S. Kristensen, and J. Levesley. Moreover...

On a theorem of V. Bernik in the metrical theory of Diophantine approximation

Classical metric Diophantine approximation revisited

The idea of using measure theoretic concepts to investigate the size of number theoretic sets, originating with E. Borel, has been used for nearly a century. It has led to the development of the theory of metrical Diophantine approximation, a branch of Number Theory which draws on a rich and broad variety of mathematics. We discuss some recent progress and open problems concerning this classica...

A Multifractal Analysis for Stern-brocot Intervals, Continued Fractions and Diophantine Growth Rates

In this paper we obtain multifractal generalizations of classical results by Lévy and Khintchin in metrical Diophantine approximations and measure theory of continued fractions. We give a complete multifractal analysis for Stern–Brocot intervals, for continued fractions and for certain Diophantine growth rates. In particular, we give detailed discussions of two multifractal spectra closely rela...