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Lower bounds for the discrepancy of inversive congruential pseudorandom numbers. (English) Zbl 0708.65006
For a short general discussion of the generators see p. 93, and 94 of [P. L’Écuyer: Random numbers for simulation, CACM 33, 86 ff. (1990)] who also explains discrepancy (informally) and its importance.
After a short definition of inverse linear congruential generators (special case of linear rational congruential generators) in the introduction, it is proved that an earlier derived lower bound for the discrepancy in the case of prime modulus p is in fact essentielly best possible. The proof requires (the full of the paper and) recourse to number theory concerning primitive polynomials over the finite field of p elements and some theorems on characters in this field. Thereby several interesting results on character sums and the number of quadratic primitive polynomials are obtained.
Reviewer: K.G.Brokate

MSC:
65C10 Random number generation in numerical analysis
11K45 Pseudo-random numbers; Monte Carlo methods
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