A NOTE ON CONTINUED FRACTIONS WITH SEQUENCES OF PARTIAL QUOTIENTS OVER THE FIELD OF FORMAL POWER SERIES

Title & Authors
A NOTE ON CONTINUED FRACTIONS WITH SEQUENCES OF PARTIAL QUOTIENTS OVER THE FIELD OF FORMAL POWER SERIES
Hu, Xuehai; Shen, Luming;

Abstract
Let $\small{\mathbb{F}_q}$ be a finite field with q elements and $\small{\mathbb{F}_q((X^{-1}))}$ be the field of all formal Laurent series with coefficients lying in $\small{\mathbb{F}_q}$. This paper concerns with the size of the set of points $\small{x{\in}\mathbb{F}_q((X^{-1}))}$ with their partial quotients $\small{A_n(x)}$ both lying in a given subset $\small{\mathbb{B}}$ of polynomials in $\small{\mathbb{F}_q[X]}$ ($\small{\mathbb{F}_q[X]}$ denotes the ring of polynomials with coefficients in $\small{\mathbb{F}_q}$) and deg $\small{A_n(x)}$ tends to infinity at least with some given speed. Write \$E_{\mathbb{B}}
Keywords
continued fractions;Laurent series;partial quotient;Hausdorff dimension;
Language
English
Cited by
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