New dimension bounds for αβ sets

Autor:	Simon Baker
Rok vydání:	2021
Předmět:	Combinatorics Set (abstract data type) Algebra and Number Theory Corollary Dimension (vector space) 010102 general mathematics 010103 numerical & computational mathematics Affine transformation 0101 mathematics Diophantine approximation 01 natural sciences Liouville number Mathematics
Zdroj:	Journal of Number Theory. 228:59-72
ISSN:	0022-314X
Popis:	In this paper we obtain new lower bounds for the upper box dimension of αβ sets. As a corollary of our main result, we show that if α is not a Liouville number and β is a Liouville number, then the upper box dimension of any αβ set is 1. We also use our dimension bounds to obtain new results on affine embeddings of self-similar sets.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::aa527ccfbd45be8afdc38808ce70b693 https://doi.org/10.1016/j.jnt.2021.04.018 Zobrazit plný text záznamu Full Text from ScienceDirect