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arXiv · 2608.15845

Weighted singular vectors in common-base self-similar sets

Taehyeong Kim·Jaemin Park
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Abstract

We prove a lower bound for the Hausdorff dimension of weighted totally irrational singular vectors in affine-spanning common-base integral self-similar sets satisfying the open set condition. For the middle-third Cantor square, the bound improves the previously known explicit lower bound.

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Taehyeong Kim, Jaemin Park. 2026-08-16. Weighted singular vectors in common-base self-similar sets. https://arxiv.org/abs/2608.15845

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