Comptes Rendus
Number Theory
Partial quotients and equidistribution
Comptes Rendus. Mathématique, Volume 349 (2011) no. 13-14, pp. 713-718.

We establish average bounds on the partial quotients of fractions b/p, with p prime, b taken in a multiplicative subgroup of (Z/pZ) 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 (modp). As a corollary, estimates on their pair correlation are refined.

Nous obtenons des bornes en moyenne pour les quotients partiels de certaines fractions b/p, p un nombre premier, b dans un sous-groupe de (Z/pZ) ainsi que pour b un élément primitif « typique » (modp). Ceci donne en particulier une amélioration de résultats de G. Larcher. Il est bien connu que le comportement des quotients partiels de bp détermine les propriétés statistiques de la distribution bj(modp). On en déduit, comme corollaire, de meilleures estimations sur les corrélations partielles pour ces suites.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2011.06.007

Mei-Chu Chang 1

1 Department of Mathematics, University of California, 900 University Avenue, Riverside, CA 92521, USA
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Mei-Chu Chang. Partial quotients and equidistribution. Comptes Rendus. Mathématique, Volume 349 (2011) no. 13-14, pp. 713-718. doi : 10.1016/j.crma.2011.06.007. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2011.06.007/

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