Limit points and discrepancy of the fractional parts of $b^n/n$
Volume 216 / 2024
Acta Arithmetica 216 (2024), 19-34
MSC: Primary 11B05; Secondary 11K38
DOI: 10.4064/aa231020-4-6
Published online: 21 August 2024
Abstract
For $b\in \mathbb N$, $b\ge 2$ we determine the limit points of a certain subsequence of $$ \bigg\{\frac{b^n}{n}\ (\bmod{1}):n\in \mathbb N\bigg\}. $$ Further, we obtain an estimate of the discrepancy of the said subsequence, improving on a result of Cilleruelo, Kumchev, Luca, Rué and Shparlinski.
