On the relative growth rate of degrees of partial quotients in continued fractions over the field of formal Laurent series

Author： Wu Jun  

Publisher： IOP Publishing

ISSN： 0951-7715

Source： Nonlinearity, Vol.22, Iss.6, 2009-06, pp. : 1303-1310

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Abstract

In this paper, we study the relative growth rate of degrees of partial quotients with respect to convergents in continued fractions over the field of Laurent series. For any r > 0, the Hausdorff dimensions of the sets {x : deg An+1(x) ≥ r · deg Qn(x) for infinitely many n} and {x : deg An+1(x) ≥ r · deg Qn(x) for all n ≥ 1} are determined, where An(x), n ≥ 1, denote the partial quotients and Qn(x), n ≥ 1, denote the denominators of the convergents.

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