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Continued fractional algebraic independence of sequences. (English) Zbl 0862.11045

A theorem of P. Bundschuh [Osaka J. Math. 25, 849-858 (1988; Zbl 0712.11041)] is used to derive a criterion that \(k\) sequences \((a_{in})_n\), \(1\leq i\leq k\), of positive real numbers are continued fractional algebraically independent. This means, by definition, that for every sequence \((c_n)_n\) of positive integers, the continued fractions \([a_{i1}c_1, a_{i2} c_2, \dots]\) are algebraically independent for \(1\leq i\leq k\).

MSC:

11J70 Continued fractions and generalizations
11J71 Distribution modulo one

Citations:

Zbl 0712.11041
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