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Sur la concentration de certaines fonctions additives

Published online by Cambridge University Press:  22 September 2011

R. DE LA BRETÈCHE  and
G. TENENBAUM
R. DE LA BRETÈCHE
Affiliation:
Institut de Mathématiques de Jussieu, Université Paris Diderot-Paris 7, UFR de Mathématiques, Case 7012, Bâtiment Chevaleret, 75205 Paris Cedex 13, France. e-mail: [email protected]
G. TENENBAUM
Affiliation:
Institut Élie Cartan, Université de Nancy 1, BP 239, 54506 Vandœuvre Cedex, France. e-mail: [email protected]
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Abstract

Improving on estimates of Erdős, Halász and Ruzsa, we provide new upper and lower bounds for the concentration function of the limit law of certain additive arithmetic functions under hypotheses involving only their average behaviour on the primes. In particular we partially confirm a conjecture of Erdős and Kátai. The upper bound is derived via a reappraisal of the method of Diamond and Rhoads, resting upon the theory of functions with bounded mean oscillation.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 152 , Issue 1 , January 2012 , pp. 179 - 189
Copyright
Copyright © Cambridge Philosophical Society 2011

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References

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