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Proceedings of the London Mathematical Society Advance Access originally published online on September 13, 2007
Proceedings of the London Mathematical Society 2008 96(1):107-135; doi:10.1112/plms/pdm029
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© 2007 London Mathematical Society

Moyennes de certaines fonctions multiplicatives sur les entiers friables, 2

Guillaume Hanrot

INRIA Lorraine
Technopôle de Nancy-Brabois
615, rue du Jardin Bo-ta-nique
54602 Villers-lès-Nancy cedex
France
Guillaume.Hanrot{at}loria.fr

Gérald Tenenbaum and Jie Wu

Institut Élie Cartan
Université Henri Poincaré–Nancy 1
BP 239
54506 Vandoeuvre cedex
France
wujie{at}iecn.u-nancy.fr

Received 10 November 2006. Revision received 22 February 2007.

We derive new, very precise estimates for averages of arithmetic functions over friable integers from analytic information on their associated Dirichlet series. These yield significant improvements upon available results in classical cases, in particular concerning the effective expansion of ‘abstract’ main terms of de Bruijn type. These results also permit new applications, linked to the solubility of polynomial equations.

2000 Mathematics Subject Classification 11N37, 11N25, 11M41, 11C08.


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