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

Harald Niederreiter; Igor E. Shparlinski

Acta Arithmetica (2000)

  • Volume: 92, Issue: 1, page 89-98
  • ISSN: 0065-1036

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Harald Niederreiter, and Igor E. Shparlinski. "Exponential sums and the distribution of inversive congruential pseudorandom numbers with prime-power modulus." Acta Arithmetica 92.1 (2000): 89-98. <http://eudml.org/doc/207371>.

@article{HaraldNiederreiter2000,
author = {Harald Niederreiter, Igor E. Shparlinski},
journal = {Acta Arithmetica},
keywords = {exponential sum; group of reduced residue classes; discrepancy; inverse congruential pseudorandom numbers},
language = {eng},
number = {1},
pages = {89-98},
title = {Exponential sums and the distribution of inversive congruential pseudorandom numbers with prime-power modulus},
url = {http://eudml.org/doc/207371},
volume = {92},
year = {2000},
}

TY - JOUR
AU - Harald Niederreiter
AU - Igor E. Shparlinski
TI - Exponential sums and the distribution of inversive congruential pseudorandom numbers with prime-power modulus
JO - Acta Arithmetica
PY - 2000
VL - 92
IS - 1
SP - 89
EP - 98
LA - eng
KW - exponential sum; group of reduced residue classes; discrepancy; inverse congruential pseudorandom numbers
UR - http://eudml.org/doc/207371
ER -

References

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  1. [1] W.-S. Chou, The period lengths of inversive congruential recursions, Acta Arith. 73 (1995), 325-341. Zbl0852.11038
  2. [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. Zbl0885.65003
  3. [3] J. Eichenauer-Herrmann and H. Niederreiter, On the discrepancy of quadratic congruential pseudorandom numbers, J. Comput. Appl. Math. 34 (1991), 243-249. Zbl0731.11046
  4. [4] J. Eichenauer-Herrmann and A. Topuzoğlu, On the period length of congruential pseudorandom number sequences generated by inversions, ibid. 31 (1990), 87-96. Zbl0704.65001
  5. [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. Zbl0958.11052
  6. [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. Zbl1011.11053
  7. [7] R. Lidl and H. Niederreiter, Finite Fields, Addison-Wesley, Reading, MA, 1983; reprint, Cambridge Univ. Press, Cambridge, 1997. Zbl0554.12010
  8. [8] H. Niederreiter, Random Number Generation and Quasi-Monte Carlo Methods, SIAM, Philadelphia, 1992. 
  9. [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. Zbl0893.11030
  10. [10] H. Niederreiter and I. E. Shparlinski, On the distribution of inversive congruential pseudorandom numbers in parts of the period, preprint, 1998. Zbl0983.11048
  11. [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. Zbl0942.11037
  12. [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. Zbl0999.11040
  13. [13] H. Salié, Über die Kloostermanschen Summen S(u,v;q), Math. Z. 34 (1932), 91-109. 
  14. [14] J. D. Vaaler, Some extremal functions in Fourier analysis, Bull. Amer. Math. Soc. (N.S.) 12 (1985), 183-216. Zbl0575.42003

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