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2000 | 92 | 1 | 89-98
Tytuł artykułu

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

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