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On the distribution of pseudo-random numbers generated by the linear congruential method. III. (English) Zbl 0342.65002

MSC:
65C10 Random number generation in numerical analysis
11J71 Distribution modulo one
11K06 General theory of distribution modulo \(1\)
65C05 Monte Carlo methods
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[1] U. Dieter, Statistical interdependence of pseudo-random numbers generated by the linear congruential method, Applications of number theory to numerical analysis (Proc. Sympos., Univ. Montréal, Montreal, Que., 1971) Academic Press, New York, 1972, pp. 287 – 317.
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[3] Donald E. Knuth, The art of computer programming. Vol. 2: Seminumerical algorithms, Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont, 1969. · Zbl 0191.18001
[4] L. Kuipers and H. Niederreiter, Uniform distribution of sequences, Wiley-Interscience [John Wiley & Sons], New York-London-Sydney, 1974. Pure and Applied Mathematics. · Zbl 0281.10001
[5] George Marsaglia, The structure of linear congruential sequences, Applications of number theory to numerical analysis (Proc. Sympos., Univ. Montreal, Montreal, Que., 1971) Academic Press, New York, 1972, pp. 249 – 285.
[6] H. G. Meijer and H. Niederreiter, Équirépartition et théorie des nombres premiers, Répartition modulo 1 (Actes Colloq., Marseille-Luminy, 1974) Springer, Berlin, 1975, pp. 104 – 112. Lecture Notes in Math., Vol. 475 (French).
[7] Harald Niederreiter, On the distribution of pseudo-random numbers generated by the linear congruential method, Math. Comp. 26 (1972), 793 – 795. · Zbl 0258.65004
[8] Harald Niederreiter, On the distribution of pseudo-random numbers generated by the linear congruential method. II, Math. Comp. 28 (1974), 1117 – 1132. , https://doi.org/10.1090/S0025-5718-1974-0457391-8 Harald Niederreiter, On the distribution of pseudo-random numbers generated by the linear congruential method. III, Math. Comp. 30 (1976), no. 135, 571 – 597. · Zbl 0303.65003
[9] H. Niederreiter, Résultats nouveaux dans la théorie quantitative de l’équirépartition, Répartition modulo 1 (Actes Colloq., Marseille-Luminy, 1974) Springer, Berlin, 1975, pp. 132 – 154. Lecture Notes in Math., Vol. 475 (French).
[10] H. Niederreiter, Some new exponential sums with applications to pseudo-random numbers, Topics in number theory (Proc. Colloq., Debrecen, 1974) North-Holland, Amsterdam, 1976, pp. 209 – 232. Colloq. Math. Soc. János Bolyai, Vol. 13.
[11] H. Niederreiter, On the cycle structure of linear recurring sequences, Math. Scand. 38 (1976), no. 1, 53 – 77. · Zbl 0325.12007
[12] H. Niederreiter and Walter Philipp, Berry-Esseen bounds and a theorem of Erdős and Turán on uniform distribution \?\?\?1, Duke Math. J. 40 (1973), 633 – 649. · Zbl 0273.10043
[13] Robert C. Tausworthe, Random numbers generated by linear recurrence modulo two, Math. Comp. 19 (1965), 201 – 209. · Zbl 0137.34804
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