Dimension conjecture for independent prime divisors
Dimension conjecture for independent prime divisors
Let be a generalized Cantor set with Hausdorff dimension , with containing at least one of and . Let be an integer such that the sets of prime divisors of and are different. Let denote the approximation exponent used in the source, with . Independent-prime-divisor dimension conjecture.
\dim_{\rm H}\bigl(W_t(\psi)\cap C(b,D)\bigr)=\max\left\\{\frac{1}{\lambda_{\psi}}+\gamma-1,0\right\\}.This dimension formula is presented as a consequence of the preceding zero-full Hausdorff-measure conjecture. Thus it is conditional on that conjecture in the source and remains conjectural itself.
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Sources & referencesView supporting material
Primary source
Bing Li, Ruofan Li and Yufeng Wu, “Zero-full law for well approximable sets in missing digit sets”, arXiv:2302.03936 (2024).
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