ON THE DIVISOR FUNCTION OVER NONHOMOGENEOUS BEATTY SEQUENCES

• Published in: Bulletin of the Australian Mathematical Society Vol. 106; no. 2; pp. 280 - 287
• Main Author: ZHANG, WEI
• Format: Journal Article
• Language: English
• Published: Cambridge, UK Cambridge University Press 01.10.2022
• Subjects: Estimates; Mathematical functions; Sequences; divisor problems; exponential sums; 11L07; 11L20; 11B83; Beatty sequences

We consider sums involving the divisor function over nonhomogeneous ( $\beta \neq 0$ ) Beatty sequences $ \mathcal {B}_{\alpha ,\beta }:=\{[\alpha n+\beta ]\}_{n=1}^{\infty } $ and show that $$ \begin{align*} \sum_{n\leq N,\ n\in\mathcal{B}_{\alpha,\beta}}d(n) =\alpha^{-1}\sum_{m\leq N}d(m) +O(N^{1-...