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Ergodic properties of some inverse polynomial series expansions of Laurent series. (English) Zbl 0774.11073
The author studies the ergodic properties of a Lüroth-type expansion of a formal Laurent series $$A$$ with coefficients in a given finite field $$F$$ with exactly $$q$$ elements. Ergodicity is with respect to Haar measure on the ideal in a power series ring over $$F$$. Since the transformation $$T$$ leading to Lüroth-type expansions is ergodic, the ergodic theorem can be utilized to obtain a large variety of strong laws. These possibilities are worked out in detail by the author. Several of the limits are functions of $$q$$, and the same function appears in seemingly unrelated expressions.

##### MSC:
 11T55 Arithmetic theory of polynomial rings over finite fields 11K55 Metric theory of other algorithms and expansions; measure and Hausdorff dimension
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##### References:
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