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Approximation orders of formal Laurent series by Oppenheim rational functions |
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| Authors: | Ai-Hua Fan Jun Wu |
| Affiliation: | a Department of Mathematics, Wuhan University, Wuhan, Hubei 430072, People's Republic of China;b LAMFA, CNRS, UMR 6140, University of Picardie Jules Verne 33, Rue Saint Leu, 80039, Amiens, France |
| Abstract: | We study formal Laurent series which are better approximated by their Oppenheim convergents. We calculate the Hausdorff dimensions of sets of Laurent series which have given polynomial or exponential approximation orders. Such approximations are faster than the approximation of typical Laurent series (with respect to the Haar measure). |
| Keywords: | Finite field Laurent series Oppenheim convergents Approximation Hausdorff dimension |
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