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Répartition Des Diviseurs Dans Les Progressions Arithmétiques

Répartition Des Diviseurs Dans Les Progressions Arithmétiques Abstract Let q and N be integers, let a be an integer coprime to q , and let zN be defined implicitly by q=(logN)log22−zN√(log2N) . We show that for large N , an integer n has at least one divisor d with q ≤ d ≤ 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. 1991 Mathematics Subject Classification 11N25, 11N37. © London Mathematical Society http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Bulletin of the London Mathematical Society Oxford University Press

Répartition Des Diviseurs Dans Les Progressions Arithmétiques

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References (6)

Publisher
Oxford University Press
Copyright
© London Mathematical Society
ISSN
0024-6093
eISSN
1469-2120
DOI
10.1112/S0024609399006773
Publisher site
See Article on Publisher Site

Abstract

Abstract Let q and N be integers, let a be an integer coprime to q , and let zN be defined implicitly by q=(logN)log22−zN√(log2N) . We show that for large N , an integer n has at least one divisor d with q ≤ d ≤ 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. 1991 Mathematics Subject Classification 11N25, 11N37. © London Mathematical Society

Journal

Bulletin of the London Mathematical SocietyOxford University Press

Published: May 1, 2000

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