On the exceptional sets in Erdös–Rényi limit theorem of β-expansion
| Autor: | Zhen-Liang Zhang, Jia Liu, Meiying Lü |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
Algebra and Number Theory
010102 general mathematics 0211 other engineering and technologies 021107 urban & regional planning 02 engineering and technology Function (mathematics) 01 natural sciences Combinatorics Erdős–Rényi model TheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGES Hausdorff dimension ComputingMethodologies_DOCUMENTANDTEXTPROCESSING Limit (mathematics) 0101 mathematics ComputingMilieux_MISCELLANEOUS Mathematics Real number |
| Zdroj: | International Journal of Number Theory. 14:1919-1934 |
| ISSN: | 1793-7310 1793-0421 |
| Popis: | Let [Formula: see text] be a real number. For any [Formula: see text], the run-length function [Formula: see text] is defined as the length of the longest run of 0’s amongst the first [Formula: see text] digits in the [Formula: see text]-expansion of [Formula: see text]. Let [Formula: see text] be a non-decreasing sequence of integers and [Formula: see text], we define [Formula: see text] In this paper, we show that the set [Formula: see text] has full Hausdorff dimension under the condition that [Formula: see text]. |
| Databáze: | OpenAIRE |
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