ON THE LARGEST DEGREE OF THE PARTIAL QUOTIENTS IN CONTINUED FRACTION EXPANSIONS OVER THE FIELD OF FORMAL LAURENT SERIES

Autor:	Luming Shen, Jian Xu, Huiping Jing
Rok vydání:	2013
Předmět:	Iterated logarithm Combinatorics Algebra and Number Theory Degree (graph theory) Laurent polynomial Laurent series Hausdorff dimension Mathematical analysis Field (mathematics) Type (model theory) Quotient Mathematics
Zdroj:	International Journal of Number Theory. :1237-1247
ISSN:	1793-7310 1793-0421
DOI:	10.1142/s1793042113500231
Popis:	For x ∈ I, let [A1(x), A2(x), …] be the continued fraction expansions over the field of Laurent series, write Ln(x) ≔ max { deg A1(x), deg A2(x), …, deg An(x)}, which is called the largest degree of partial quotients. In this paper, we give an iterated logarithm type theorem for Ln(x), and by which, we get that for P-almost all x ∈ I, [Formula: see text]. Also the Hausdorff dimensions of the related exceptional sets are determined.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::e3b10e8ef993c209a28f0cf706bd817d https://doi.org/10.1142/s1793042113500231 Zobrazit plný text záznamu