Abstract
We establish average bounds on the partial quotients of fractions b / p , with p prime, b taken in a multiplicative subgroup of ( Z / p Z ) ⁎ and for “most” primitive elements b. Our result improves upon earlier work due to G. Larcher. The behavior of the partial quotients of b / p is well known to be crucial to the statistical properties of the pseudo-congruential number generator ( mod p ) . As a corollary, estimates on their pair correlation are refined.
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