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

- Journal title : Bulletin of the Korean Mathematical Society
- Volume 49, Issue 4, 2012, pp.875-883
- Publisher : The Korean Mathematical Society
- DOI : 10.4134/BKMS.2012.49.4.875

Title & Authors

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

Hu, Xuehai; Shen, Luming;

Hu, Xuehai; Shen, Luming;

Abstract

Let be a finite field with q elements and be the field of all formal Laurent series with coefficients lying in . This paper concerns with the size of the set of points with their partial quotients both lying in a given subset of polynomials in ( denotes the ring of polynomials with coefficients in ) and deg tends to infinity at least with some given speed. Write . It was shown in [8] that the Hausdorff dimension of is inf{ < }. In this note, we will show that the above result is sharp. Moreover, we also attempt to give conditions under which the above dimensional formula still valid if we require the given speed of deg tends to infinity.

Keywords

continued fractions;Laurent series;partial quotient;Hausdorff dimension;

Language

English

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