Dimension of level sets in GCF expansion with parameters
| Autor: | Kunkun Song, Yuanyang Chang |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
Algebra and Number Theory
010102 general mathematics Mathematical analysis Dimension (graph theory) 0102 computer and information sciences Function (mathematics) 01 natural sciences Combinatorics 010201 computation theory & mathematics Hausdorff dimension 0101 mathematics Generalized continued fraction Quotient Mathematics |
| Zdroj: | Journal of Number Theory. 180:743-755 |
| ISSN: | 0022-314X |
| DOI: | 10.1016/j.jnt.2017.06.002 |
| Popis: | Let k n ( x ) be the n -th partial quotient of the generalized continued fraction (GCF) expansion of x . This paper is concerned with the growth rate of k n ( x ) . When the parameter function satisfies − 1 ϵ ( k ) ≤ 1 , we obtain the Hausdorff dimension of the sets E ϕ = { x ∈ ( 0 , 1 ) : lim n → ∞ log k n ( x ) ϕ ( n ) = 1 } for any nondecreasing ϕ with lim n → ∞ ( ϕ ( n + 1 ) − ϕ ( n ) ) = ∞ and lim n → ∞ ϕ ( n + 1 ) / ϕ ( n ) = 1 . Applications are given to several kinds of exceptional sets related to the GCF expansion. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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