On the distribution of inversive congruential pseudorandom numbers in parts of the period (Q2723529)

The authors present bounds on the discrepancy of individual sequences of inversive congruential pseudorandom numbers in parts of the period. The proof is based on a new bound for certain incomplete exponential sums. In an earlier work [Finite Fields Appl. 5, 246--253 (1999; Zbl 0942.11037)] the authors have obtained similar results for generators \(u_{n+1}= f(u_n)\), where \(f\) is a polynomial over \(\mathbb Z/p\mathbb Z\). For the special case \(f(x)= x^e\) an alternative approach is due to \textit{J. B. Friedlander, D. Lieman} and \textit{I. Shparlinski} [Sequences and their applications, SETA '98, Singapore 1998, Springer Series in Discrete Mathematics and Theoretical Computer Science, London, 205--212 (1999; Zbl 1013.11047)].