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Length of the powers of a rational fraction. (English) Zbl 0878.11028

Let \(k\) be a field and let \(\alpha\) be a rational fraction of \(k(x)\) whose continued fraction expansion is \([a_0,a_1,\dots, a_s]\), with length \(D(\alpha)= s+1\). In the paper under review, the author shows that \(D(\alpha^n)\) tends to infinity with \(n\) provided the characteristic of \(k\) is 0, \(\alpha\) is not a polynomial nor the reciprocal of a polynomial. The author also deals with the case of non-zero characteristic.

MSC:

11J70 Continued fractions and generalizations
11A55 Continued fractions
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References:

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