The number of steps in the euclidean algorithm over complex quadratic fields |
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| Authors: | Arnold Knopfmacher John Knopfmacher |
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| Affiliation: | (1) Dept of Computational & Applied Mathematics, University of the Witwatersrand, P.O. Wits 2050, Johannesburg, South Africa;(2) Dept. of Mathematics, University of the Witwatersrand, P.O. Wits 2050, Johannesburg, South Africa |
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| Abstract: | We obtain upper and lower bounds for the number of divisions in the Euclidean algorithm, for almost all pairs of algebraic integers lying in the complex quadratic fields   (–m), form=1, 2, 3, 7 and 11. In addition, the order of the average length for almost all such pairs is deduced. |
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| Keywords: | 11R11 13F07 |
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