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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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