| Institution: | (1) Department of Mathematics, Wuhan University, Wuhan, Hubei 430072, P. R. China and LAMFA, CNRS, UMR 6140, University of Picardie Jules Verne, 33 Rue Saint Leu, 80039 Amiens, France |
| Abstract: | We investigate metric properties of the polynomial digits occurring in a large class of Oppenheim expansions of Laurent series, including Lüroth, Engel, and Sylvester expansions of Laurent series and Cantor infinite products of Laurent series. The obtained results cover those for special cases of Lüroth and Engel expansions obtained by Grabner, A. Knopfmacher, and J. Knopfmacher. Our results applied in the cases of Sylvester expansions and Cantor infinite products are original. We also calculate the Hausdorff dimensions of different exceptional sets on which the above-mentioned metric properties fail to hold. |
