paper

Convergence exponent of Pierce expansion digit sequences

arXiv:2309.01722 · doi:10.1142/S1793042125500952

Abstract

In this paper, we investigate the convergence exponent of Pierce expansion digit sequences. We explore some basic properties of the convergence exponent as a real-valued function defined on the closed unit interval, as well as those of the level sets of the function. Additionally, we further study subsets of the closed unit interval on which the series of positive th powers of the reciprocals of the Pierce expansion digits diverges.

28 pages, typos corrected

Convergence exponent of Pierce expansion digit sequences · wovepaper