Kloosterman-type sums and the discrepancy of nonoverlapping pairs of inversive congruential pseudorandom numbers

Jürgen Eichenauer-Herrmann; Harald Niederreiter

Acta Arithmetica (1993)

  • Volume: 65, Issue: 2, page 185-194
  • ISSN: 0065-1036

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Jürgen Eichenauer-Herrmann, and Harald Niederreiter. "Kloosterman-type sums and the discrepancy of nonoverlapping pairs of inversive congruential pseudorandom numbers." Acta Arithmetica 65.2 (1993): 185-194. <http://eudml.org/doc/206570>.

@article{JürgenEichenauer1993,
author = {Jürgen Eichenauer-Herrmann, Harald Niederreiter},
journal = {Acta Arithmetica},
keywords = {Kloosterman-type exponential sum; inverse congruential sequence; inverse congruential pseudorandom numbers; discrepancy},
language = {eng},
number = {2},
pages = {185-194},
title = {Kloosterman-type sums and the discrepancy of nonoverlapping pairs of inversive congruential pseudorandom numbers},
url = {http://eudml.org/doc/206570},
volume = {65},
year = {1993},
}

TY - JOUR
AU - Jürgen Eichenauer-Herrmann
AU - Harald Niederreiter
TI - Kloosterman-type sums and the discrepancy of nonoverlapping pairs of inversive congruential pseudorandom numbers
JO - Acta Arithmetica
PY - 1993
VL - 65
IS - 2
SP - 185
EP - 194
LA - eng
KW - Kloosterman-type exponential sum; inverse congruential sequence; inverse congruential pseudorandom numbers; discrepancy
UR - http://eudml.org/doc/206570
ER -

References

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  1. [1] J. Eichenauer, J. Lehn and A. Topuzoğlu, A nonlinear congruential pseudorandom number generator with power of two modulus, Math. Comp. 51 (1988), 757-759. Zbl0701.65008
  2. [2] J. Eichenauer-Herrmann, Inversive congruential pseudorandom numbers: a tutorial, Internat. Statist. Rev. 60 (1992), 167-176. Zbl0766.65002
  3. [3] J. Eichenauer-Herrmann, On the autocorrelation structure of inversive congruential pseudorandom number sequences, Statist. Papers 33 (1992), 261-268. Zbl0766.65001
  4. [4] J. Eichenauer-Herrmann, H. Grothe, H. Niederreiter and A. Topuzoğlu, On the lattice structure of a nonlinear generator with modulus 2 α , J. Comput. Appl. Math. 31 (1990), 81-85. Zbl0702.65006
  5. [5] J. Eichenauer-Herrmann and H. Niederreiter, Lower bounds for the discrepancy of inversive congruential pseudorandom numbers with power of two modulus, Math. Comp. 58 (1992), 775-779. Zbl0762.65001
  6. [6] J. Kiefer, On large deviations of the empiric d.f. of vector chance variables and a law of the iterated logarithm, Pacific J. Math. 11 (1961), 649-660. Zbl0119.34904
  7. [7] H. Niederreiter, The serial test for congruential pseudorandom numbers generated by inversions, Math. Comp. 52 (1989), 135-144. Zbl0657.65007
  8. [8] H. Niederreiter, Recent trends in random number and random vector generation, Ann. Oper. Res. 31 (1991), 323-345. Zbl0737.65001
  9. [9] H. Niederreiter, Nonlinear methods for pseudorandom number and vector generation, in: Simulation and Optimization, G. Pflug and U. Dieter (eds.), Lecture Notes in Economics and Math. Systems 374, Springer, Berlin, 1992, 145-153 . Zbl0849.11055
  10. [10] H. Niederreiter, Random Number Generation and Quasi-Monte Carlo Methods, SIAM, Philadelphia, 1992. Zbl0761.65002
  11. [11] H. Niederreiter, Pseudorandom numbers and quasirandom points, Z. Angew. Math. Mech., to appear. Zbl0796.11028

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