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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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Lower bounds for the discrepancy of inversive congruential pseudorandom numbers
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by Harald Niederreiter PDF
Math. Comp. 55 (1990), 277-287 Request permission

Abstract:

The inversive congruential method is a uniform pseudorandom number generator which was introduced recently. For a prime modulus p the discrepancy $D_p^{(k)}$ of k-tuples of successive pseudorandom numbers generated by this method determines the statistical independence properties of these pseudorandom numbers. It was shown earlier by the author that \[ D_p^{(k)} = O({p^{ - 1/2}}{(\log p)^k})\quad {\text {for}}\;2 \leq k < p.\] Here it is proved that this bound is essentially best possible. In fact, for a positive proportion of the admissible parameters in the inversive congruential method the discrepancy $D_p^{(k)}$ is at least of the order of magnitude ${p^{ - 1/2}}$ for all $k \geq 2$.
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Additional Information
  • © Copyright 1990 American Mathematical Society
  • Journal: Math. Comp. 55 (1990), 277-287
  • MSC: Primary 65C10; Secondary 11K45
  • DOI: https://doi.org/10.1090/S0025-5718-1990-1023766-0
  • MathSciNet review: 1023766