Approximation orders of formal Laurent series by Oppenheim rational functions

✍ Scribed by Ai-Hua Fan; Jun Wu

• Publisher: Elsevier Science
• Year: 2003
• Tongue: English
• Weight: 204 KB
• Volume: 121
• Category: Article
• ISSN: 0021-9045
• DOI: 10.1016/s0021-9045(02)00064-3

✦ Synopsis

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).