2007
DOI: 10.1016/j.ffa.2005.05.003
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Hausdorff dimensions of bounded-type continued fraction sets of Laurent series

Abstract: We study the Hausdorff dimensions of bounded-type continued fraction sets of Laurent series and show that the Texan conjecture is true in the case of Laurent series.

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Cited by 11 publications
(5 citation statements)
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“…those arising from the family of Japanese continued fractions, named for Hitoshi Nakada, Shunji Ito, and Shigeru Tanaka -see [11,16,24,61] for these systems and some variations. Furthermore, continued fraction algorithms arising from study of geodesic flows on negatively curved surfaces [10,55], and continued fraction expansions over the field of Laurent series [9,46,78,85] would be natural environs to investigate analogues of our results.…”
Section: Directions To Further Researchmentioning
confidence: 99%
“…those arising from the family of Japanese continued fractions, named for Hitoshi Nakada, Shunji Ito, and Shigeru Tanaka -see [11,16,24,61] for these systems and some variations. Furthermore, continued fraction algorithms arising from study of geodesic flows on negatively curved surfaces [10,55], and continued fraction expansions over the field of Laurent series [9,46,78,85] would be natural environs to investigate analogues of our results.…”
Section: Directions To Further Researchmentioning
confidence: 99%
“…We prove (13) by induction. For 1 n n 0 , (13) holds by the definition of W . When n > n 0 , by ( 12) and lemma 2.1, using induction on n, we have…”
Section: Thus S B (E M (R B)) ⊂ E(r) and This Implies Dim H S B (E M ...mentioning
confidence: 99%
“…This result was generalized by the author in [13]. Let S be a non-empty finite set of polynomials with strictly positive degree and coefficients lying in F q , say S = {B 1 , B 2 , .…”
Section: Introductionmentioning
confidence: 98%
“…Schmidt [15], Berthé and Nakada [4]). For results on the dimension theory, we refer to Niederreiter and Vielhaber [10,11], Wu [16], Hu, Wang, Wu and Yu [8].…”
Section: Introductionmentioning
confidence: 99%