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ArticleOriginal scientific text

Title

Exponential sums and the distribution of inversive congruential pseudorandom numbers with prime-power modulus

Authors 1, 2

Affiliations

  1. Institute of Discrete Mathematics, Austrian Academy of Sciences, Sonnenfelsgasse 19, A-1010 Vienna, Austria
  2. Department of Computing, Macquarie University, Sydney, NSW 2109, Australia

Bibliography

  1. W.-S. Chou, The period lengths of inversive congruential recursions, Acta Arith. 73 (1995), 325-341.
  2. J. Eichenauer-Herrmann, E. Herrmann and S. Wegenkittl, A survey of quadratic and inversive congruential pseudorandom numbers, in: Monte Carlo and Quasi-Monte Carlo Methods 1996, H. Niederreiter et al. (eds.), Lecture Notes in Statist. 127, Springer, New York, 1998, 66-97.
  3. J. Eichenauer-Herrmann and H. Niederreiter, On the discrepancy of quadratic congruential pseudorandom numbers, J. Comput. Appl. Math. 34 (1991), 243-249.
  4. J. Eichenauer-Herrmann and A. Topuzoğlu, On the period length of congruential pseudorandom number sequences generated by inversions, ibid. 31 (1990), 87-96.
  5. F. Griffin, H. Niederreiter and I. E. Shparlinski, On the distribution of nonlinear recursive congruential pseudorandom numbers of higher orders, in: Proc. 13th Sympos. on Appl. Algebra, Algebraic Algorithms, and Error-Correcting Codes, Hawaii, 1999, Lecture Notes in Comput. Sci., Springer, Berlin, to appear.
  6. J. Gutierrez, H. Niederreiter and I. E. Shparlinski, On the multidimensional distribution of inversive congruential pseudorandom numbers in parts of the period, Monatsh. Math., to appear.
  7. R. Lidl and H. Niederreiter, Finite Fields, Addison-Wesley, Reading, MA, 1983; reprint, Cambridge Univ. Press, Cambridge, 1997.
  8. H. Niederreiter, Random Number Generation and Quasi-Monte Carlo Methods, SIAM, Philadelphia, 1992.
  9. H. Niederreiter, New developments in uniform pseudorandom number and vector generation, in: Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing, H. Niederreiter and P.J.-S. Shiue (eds.), Lecture Notes in Statist. 106, Springer, New York, 1995, 87-120.
  10. H. Niederreiter and I. E. Shparlinski, On the distribution of inversive congruential pseudorandom numbers in parts of the period, preprint, 1998.
  11. H. Niederreiter and I. E. Shparlinski, On the distribution and lattice structure of nonlinear congruential pseudorandom numbers, Finite Fields Appl. 5 (1999), 246-253.
  12. H. Niederreiter and I. E. Shparlinski, On the distribution of pseudorandom numbers and vectors generated by inversive methods, Appl. Algebra Engrg. Comm. Comput., to appear.
  13. H. Salié, Über die Kloostermanschen Summen S(u,v;q), Math. Z. 34 (1932), 91-109.
  14. J. D. Vaaler, Some extremal functions in Fourier analysis, Bull. Amer. Math. Soc. (N.S.) 12 (1985), 183-216.
Acta Arithmetica
2000/92/1
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Pages:
89-98
Main language of publication
English
Received
1999-06-11
Published
2000
Exact and natural sciences