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On the discrepancy of inversive congruential pseudorandom numbers with prime power modulus, II

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Abstract

One of the alternatives to linear congruential pseudorandom number generators with their known deficiencies is the inversive congruential method with prime power modulus. Recently, it was proved that pairs of inversive congruential pseudorandom numbers have nice statistical independence properties. In the present paper it is shown that a similar result cannot be obtained fork-tuples withk≥3 since their discrepancy is too large. The method of proof relies on the evaluation of certain exponential sums. In view of the present result the inversive congruential method with prime power modulus seems to be not absolutely suitable for generating uniform pseudorandom numbers.

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  1. Fachbereich Mathematik Technische Hochschule, Schloßgartenstraße 7, D-6100, Darmstadt, FRG

    Jürgen Eichenauer-Herrmann

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  1. Jürgen Eichenauer-Herrmann
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Eichenauer-Herrmann, J. On the discrepancy of inversive congruential pseudorandom numbers with prime power modulus, II. Manuscripta Math 79, 239–246 (1993). https://doi.org/10.1007/BF02568342

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  • DOI: https://doi.org/10.1007/BF02568342

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