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Dimension bounds for singular affine forms
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DOI：10.1112/mtk.70084.png)
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Abstract
En 中文
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 Urba & nacute;ski, 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.
Keywords:
HAUSDORFF DIMENSION
DIOPHANTINE APPROXIMATION
EXPONENTS
Journal
M
IF:
0.8
Papers:
45
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0