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

Abstract

The inversive congruential method for generating uniform pseudorandom numbers has been introduced recently as an alternative to linear congruential generators with their coarse lattice structure. In the present paper the statistical independence properties of pairs of consecutive pseudorandom numbers obtained from an inversive congruential generator with prime power modulus are analysed by means of the serial test. Upper bounds for the discrepancy of these pairs are established which are essentially best possible. The results show that the inversive congruential method with prime power modulus performs uniformly satisfactorily under the serial test. The methods of proof rely heavily on the evaluation of certain exponential sums which resemble Kloosterman sums.

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Eichenauer-Herrmann, J. On the discrepancy of inversive congruential pseudorandom numbers with prime power modulus. Manuscripta Math 71, 153–161 (1991). https://doi.org/10.1007/BF02568399

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  • DOI: https://doi.org/10.1007/BF02568399

Keywords

  • Serial Test
  • Pseudorandom Number
  • Congruential Generator
  • Congruential Method
  • Linear Congruential Generator