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- W2131107582 abstract "Abstract For any positive integer q ≧2, let F q be a finite field with q elements, F q (( z -1 )) be the field of all formal Laurent series in an inderminate z, I denote the valuation ideal z -1 F q [[ z -1 ]] in the ring of formal power series F q (( z -1 )) normalized by P( l ) = 1. For any x ∈ I , let the series be the Engel expansin of Laurent series of x . Grabner and Knopfmacher have shown that the P-measure of the set A(α) = { x ∞ I : lim n →∞ deg a n (x )/n = ά} is l when α = q/(q -l), where deg a n ( x ) is the degree of polynomial a n ( x ). In this paper, we prove that for any α ≧ l, A (α) has Hausdorff dimension l. Among other thing we also show that for any integer m , the following set B(m) = { x ∈ l: deg a n+1 ( x ) - deg a n ( x ) = m for any n ≧ l} has Hausdorff dimension 1." @default.
- W2131107582 created "2016-06-24" @default.
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- W2131107582 date "2003-08-01" @default.
- W2131107582 modified "2023-10-18" @default.
- W2131107582 title "Engel Series Expansions of Laurent Series and Hausdorff Dimensions" @default.
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- W2131107582 doi "https://doi.org/10.1017/s1446788700003438" @default.
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