Cantor sets determined by partial quotients of continued fractions of Laurent series

AbstractIn this paper, two types of general sets determined by partial quotients of continued fractions over the field of formal Laurent series with coefficients from a given finite field are studied. The Hausdorff dimensions of {x:degAn(x)⩾ϕ(n),for infinitely many n} and {x:degAn(x)⩾ϕ(n),∀n⩾1} are determined completely, where An(x) denotes the partial quotients in the continued fraction expansion (in case of Laurent series) of x and ϕ(n) is a positive valued function defined on natural numbers N