Weighted singular vectors in common-base self-similar sets

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.

15 pages, 2 figures, 1 table. Corrected cross-reference labels for definitions, lemmas, and corollaries; no changes to mathematical results