Dimension bounds for singular affine forms
Abstract
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.
Fields of Study & Subjects
Matrix Theory and Algorithms
Publication details
- Journal / source
- Mathematika
- Volume
- 72
- Issue
- 2
- Publication date
- 1 April 2026
- Language
- EN