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Multi-continued fraction algorithm on multi-formal Laurent series. (English) Zbl 1146.11036
There has been several attempts to extend continued fraction expansions of reals to number fields. The best known in the literature is the Jacobi-Perron algorithm. While the Jacobi-Perron algorithm leads to good approximations, it does not provide the best rational approximation in general. The authors in the present paper introduce a new continued fraction algorithm for multiformal Laurent series. It is proved that this algorithm guarantees the best rational approximations for multi-formal Laurent series. The authors devote a section to definitions, then a section states the main results of the paper. The paper is closed with a section containing the proofs.

11J70 Continued fractions and generalizations
11A55 Continued fractions
11K50 Metric theory of continued fractions
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