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RÉPARTITION DES DIVISEURS DANS LES PROGRESSIONS ARITHMÉTIQUES

Published online by Cambridge University Press:  01 May 2000

R. DE LA BRETÈCHE
R. DE LA BRETÈCHE
Affiliation:
Département de Mathématiques, UMR 8628 CNRS-Université, Université de Paris-Sud, bât. 425, F-91405 Orsay, France
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Abstract

Let q and N be integers, let a be an integer coprime to q, and let zN be defined implicitly by q = (log N)log22−ZN √(log2N). We show that for large N, an integer n has at least one divisor d with q [les ] d [les ] N and d ≡ a(mod q) with probability approximately Φ(zN), where Φ denotes the distribution function of the Gaussian Law. This solves a conjecture of Hall.

Type
NOTES AND PAPERS
Information
Bulletin of the London Mathematical Society , Volume 32 , Issue 3 , May 2000 , pp. 257 - 262
Copyright
© The London Mathematical Society 2000

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