Year: 2026
Type: preprint
Abstract: In this paper, we investigate whether Harper's better than square-root cancellation phenomenon still appears in Piatetski-Shapiro sequences, and when one should expect only square-root size. If $c=c(X)$ satisfies $(c-1)\log X\to 0$ as $X\to\infty$, then for Steinhaus or Rademacher random multiplicative functions we have \[ \mathbb{E}\left|\sum_{n\in\mathcal{N}^{(c)}(X)}f(n)\right|=o\!\left(\sqrt{|\mathcal{N}^{(c)}(X)|}\right). \] For Lebesgue almost every fixed $1
Source: arXiv (Cornell University)
Authors: Zhu, Renjie, Zhang, Tianping
Institutions: Northwest University, Shaanxi Normal University
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7203710312