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On the distribution of pseudo-random numbers generated by the linear congruential method. (English) Zbl 0258.65004

MSC:
65C10 Random number generation in numerical analysis
11J71 Distribution modulo one
65D30 Numerical integration
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References:
[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.
[2] D. L. Jagerman, Some theorems concerning pseudo-random numbers, Math. Comp. 19 (1965), 418 – 426. · Zbl 0154.04803
[3] J. F. Koksma, A general theorem from the theory of uniform distribution modulo 1, Mathematica, Zutphen. B. 11 (1942), 7 – 11 (Dutch). · Zbl 0026.38803
[4] H. Niederreiter, Methods for estimating discrepancy, Applications of number theory to numerical analysis (Proc. Sympos., Univ. Montréal, Montreal, Que., 1971) Academic Press, New York, 1972, pp. 203 – 236.
[5] H. Niederreiter, Almost-arithmetic progressions and uniform distribution, Trans. Amer. Math. Soc. 161 (1971), 283 – 292. · Zbl 0219.10040
[6] H. Niederreiter, Discrepancy and convex programming, Ann. Mat. Pura Appl. (4) 93 (1972), 89 – 97. · Zbl 0281.10027
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