J. Aust. Math. Soc.  75 (2003), 1-7
Engel series expansions of Laurent series and Hausdorff dimensions

 Jun Wu   Department of Mathematics   Wuhan University   Wuhan, Hubei, 430072   People's Republic of China  wujunyu@public.wh.hb.cn

Abstract
For any positive integer , let be a finite field with elements, be the field of all formal Laurent series in an indeterminate , denote the valuation ideal in the ring of formal power series and P denote probability measure with respect to the Haar measure on normalized by . For any , let the series
be the Engel expansion of Laurent series of . Grabner and Knopfmacher have shown that the P-measure of the set
is 1 when , where is the degree of polynomial . In this paper, we prove that for any , has Hausdorff dimension 1. Among other things we also show that for any positive integer , the following set
has Hausdorff dimension 1.