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On the normal concentration of divisors, 2

Published online by Cambridge University Press:  06 July 2009

HELMUT MAIER  and
GÉRALD TENENBAUM
HELMUT MAIER
Affiliation:
Universitát Ulm, Abt. Mathematik III, Helmholtzstrasse 18, D-89069 Ulm, Germany
GÉRALD TENENBAUM
Affiliation:
Institut Élie Cartan, Nancy-Université, CNRS, INRIA, Boulevard des Aiguillettes, BP 239, 54506 Vandœuvre Cedex, France
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Abstract

We improve the current upper and lower bounds for the normal order of the Erdős–Hooley Δ–functionobtaining, for almost all integers n, the inequalitieswhere the exponent γ := (log 2)/log((1−1/log 27)/(1 − 1/log 3)) ≈ 0.33827 is conjectured to be optimal.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 147 , Issue 3 , November 2009 , pp. 513 - 540
Copyright
Copyright © Cambridge Philosophical Society 2009

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References

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