The relative growth rate for the digits in Lüroth expansions

Abstract

In this note, the rate of growth of digits in the Lüroth expansion of an irrational number is studied relative to the rate of approximation of the number by its convergents. The Hausdorff dimension of exceptional sets of points with a given relative growth rate is established.

Keywords

• Lüroth expansion
• Hausdorff dimension
• relative growth rate