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Metric properties of Engel series expansions of Laurent series. (English) Zbl 0939.11029
The authors define for a formal Laurent series over finite field its “Engel type” expansion. Then they define a probability measure on the valuation ideal, using the Haar measure on the ring of all formal Laurent series. In Theorem 1 are stated some results for almost all elements of this valuation ideal, concerning “digits” of this “Engel type” expansion. Theorem 2 gives another type of probabilistic results for these digits. The proofs are based on the probabilistic methods used in the valuation ideal equipped with a probability measure.

##### MSC:
 11K55 Metric theory of other algorithms and expansions; measure and Hausdorff dimension 11T06 Polynomials over finite fields
##### Keywords:
Engel series; Laurent series; finite field; metric result
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##### References:
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