Discrepancy estimates related to the fractional parts of $b^n/n$

TL;DR

This paper provides a new discrepancy estimate for the fractional parts of the sequence b^n/n, advancing understanding of their distribution and improving previous results.

Contribution

It introduces an improved discrepancy estimate for the fractional parts of b^n/n, refining earlier bounds by Cilleruelo et al.

Findings

Enhanced discrepancy bounds for fractional parts of b^n/n

Improved understanding of distribution properties of the sequence

Advancement over previous results by Cilleruelo et al.

Abstract

We prove a discrepancy estimate related to the sequence of fractional parts of $b^n/n$. This improves an earlier result of Cilleruelo et al.