




















Abstract:We formulate a notion of square-root cancellation for the operator which sums a mean-zero function over a rotating hyperplane in $R^d$, where $R$ is a possibly noncommutative finite ring. Using an argument due to Hart, Iosevich, Koh, and Rudnev, we show that this square-root cancellation occurs uniformly when $R$ is a finite field. We then show that this square-root cancellation cannot occur uniformly over families of finite rings which are not eventually finite fields. This extends an earlier result of the author to a non-translation-invariant operator.
From: Nathaniel Kingsbury-Neuschotz [view email]
[v1]
Tue, 1 Apr 2025 02:27:39 UTC (19 KB)
[v2]
Mon, 28 Jul 2025 19:16:02 UTC (20 KB)
[v3]
Mon, 29 Jun 2026 02:29:13 UTC (20 KB)
此内容由惯性聚合(RSS阅读器)自动聚合整理,仅供阅读参考。 原文来自 — 版权归原作者所有。