Kloosterman-type sums and the discrepancy of nonoverlapping pairs of inversive congruential pseudorandom numbers
Jürgen Eichenauer-Herrmann ; Harald Niederreiter
Acta Arithmetica, Tome 64 (1993), p. 185-194 / Harvested from The Polish Digital Mathematics Library
Publié le : 1993-01-01
EUDML-ID : urn:eudml:doc:206570
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     author = {J\"urgen Eichenauer-Herrmann and Harald Niederreiter},
     title = {Kloosterman-type sums and the discrepancy of nonoverlapping pairs of inversive congruential pseudorandom numbers},
     journal = {Acta Arithmetica},
     volume = {64},
     year = {1993},
     pages = {185-194},
     zbl = {0785.11043},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-aav65i2p185bwm}
}
Jürgen Eichenauer-Herrmann; Harald Niederreiter. Kloosterman-type sums and the discrepancy of nonoverlapping pairs of inversive congruential pseudorandom numbers. Acta Arithmetica, Tome 64 (1993) pp. 185-194. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-aav65i2p185bwm/

[000] [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. | Zbl 0701.65008

[001] [2] J. Eichenauer-Herrmann, Inversive congruential pseudorandom numbers: a tutorial, Internat. Statist. Rev. 60 (1992), 167-176. | Zbl 0766.65002

[002] [3] J. Eichenauer-Herrmann, On the autocorrelation structure of inversive congruential pseudorandom number sequences, Statist. Papers 33 (1992), 261-268. | Zbl 0766.65001

[003] [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. | Zbl 0702.65006

[004] [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. | Zbl 0762.65001

[005] [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. | Zbl 0119.34904

[006] [7] H. Niederreiter, The serial test for congruential pseudorandom numbers generated by inversions, Math. Comp. 52 (1989), 135-144. | Zbl 0657.65007

[007] [8] H. Niederreiter, Recent trends in random number and random vector generation, Ann. Oper. Res. 31 (1991), 323-345. | Zbl 0737.65001

[008] [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 . | Zbl 0849.11055

[009] [10] H. Niederreiter, Random Number Generation and Quasi-Monte Carlo Methods, SIAM, Philadelphia, 1992. | Zbl 0761.65002

[010] [11] H. Niederreiter, Pseudorandom numbers and quasirandom points, Z. Angew. Math. Mech., to appear. | Zbl 0796.11028