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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

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

The 2020 MCQ for Mathematics of Computation is 1.78.

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On the average distribution of pseudorandom numbers generated by nonlinear permutations
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by Igor E. Shparlinski PDF
Math. Comp. 80 (2011), 1053-1061 Request permission


We modify the approach of H. Niederreiter and I. E. Shparlinski and improve one of their results on the distribution of inversive congruential pseudorandom numbers over a finite field for almost all initial values. However the main application of the new method is a similar result for pseudorandom numbers generated by iterations of a nonlinear permutation polynomial over a finite field, to which the original approach of H. Niederreiter and I. E. Shparlinski does not apply.
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Additional Information
  • Igor E. Shparlinski
  • Affiliation: Department of Computing, Macquarie University, NSW 2109, Australia
  • MR Author ID: 192194
  • Email:
  • Received by editor(s): July 9, 2009
  • Received by editor(s) in revised form: December 21, 2009
  • Published electronically: August 31, 2010
  • Additional Notes: The author was supported in part by ARC Grant┬áDP0881473
  • © Copyright 2010 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Math. Comp. 80 (2011), 1053-1061
  • MSC (2010): Primary 11K45, 11T23, 65C10
  • DOI:
  • MathSciNet review: 2772110