Dimension bounds for singular affine forms

IF 0.8 3区数学 Q2 MATHEMATICS

Mathematika Pub Date : 2026-04-03 DOI:10.1112/mtk.70084

Gaurav Aggarwal

引用次数: 0

Abstract

In this paper, we establish upper bounds on the dimension of sets of singular-on-average and -singular affine forms in singly metric settings where either the matrix or the shift is fixed. These results partially address open questions posed by Das, Fishman, Simmons, and Urbański, as well as Kleinbock and Wadleigh. Furthermore, we extend our results to the generalized weighted setup and derive bounds for the intersection of these sets with a wide class of fractals.

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奇异仿射形式的维限

本文建立了单度量环境下矩阵或位移固定的奇异平均仿射形式集和-奇异仿射形式集的维数上界。这些结果部分解决了Das、Fishman、Simmons和Urbański以及kleinbok和Wadleigh提出的开放性问题。进一步，我们将我们的结果推广到广义加权设置，并推导出这些集合与一类广泛的分形相交的界。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Mathematika MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

1.40

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Mathematika publishes both pure and applied mathematical articles and has done so continuously since its founding by Harold Davenport in the 1950s. The traditional emphasis has been towards the purer side of mathematics but applied mathematics and articles addressing both aspects are equally welcome. The journal is published by the London Mathematical Society, on behalf of its owner University College London, and will continue to publish research papers of the highest mathematical quality.