Download PDF - Kloosterman-type sums and the discrepancy of nonoverlapping pairs of inversive congruential pseudorandom numbersAll rights reserved. Copyright exceptions and limitations apply

ArticleOriginal scientific text

Title

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

Authors 1, 2

Affiliations

  1. Fachbereich Mathematik, Technische Hochschule Darmstadt, Schlossgartenstrasse 7, D-64289 Darmstadt, F.R.G.
  2. Institut für Informationsverarbeitung, Österreichische Akademie, der Wissenschaften, Sonnenfelsgasse 19, A-1010 Wien, Austria

Bibliography

  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.
  2. J. Eichenauer-Herrmann, Inversive congruential pseudorandom numbers: a tutorial, Internat. Statist. Rev. 60 (1992), 167-176.
  3. J. Eichenauer-Herrmann, On the autocorrelation structure of inversive congruential pseudorandom number sequences, Statist. Papers 33 (1992), 261-268.
  4. J. Eichenauer-Herrmann, H. Grothe, H. Niederreiter and A. Topuzoğlu, On the lattice structure of a nonlinear generator with modulus 2α, J. Comput. Appl. Math. 31 (1990), 81-85.
  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.
  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.
  7. H. Niederreiter, The serial test for congruential pseudorandom numbers generated by inversions, Math. Comp. 52 (1989), 135-144.
  8. H. Niederreiter, Recent trends in random number and random vector generation, Ann. Oper. Res. 31 (1991), 323-345.
  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 .
  10. H. Niederreiter, Random Number Generation and Quasi-Monte Carlo Methods, SIAM, Philadelphia, 1992.
  11. H. Niederreiter, Pseudorandom numbers and quasirandom points, Z. Angew. Math. Mech., to appear.
Acta Arithmetica
1993/65/2
Export to PBN, Opens in new tab
Pages:
185-194
Main language of publication
English
Received
1993-03-17
Published
1993
Exact and natural sciences