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Sur les processus arithmétiques liés aux diviseurs

  • R. de la Bretèche (a1) and G. Tenenbaum (a2)

Abstract

For natural integer n, let D n denote the random variable taking the values log d for d dividing n with uniform probability 1/τ(n). Then t↦ℙ(D n n t ) (0≤t≤1) is an arithmetic process with respect to the uniform probability over the first N integers. It is known from previous works that this process converges to a limit law and that the same holds for various extensions. We investigate the generalized moments of arbitrary orders for the limit laws. We also evaluate the mean value of the two-dimensional distribution function ℙ(D n n u , D{n/D n }n v ).

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Corresponding author

Université Paris Diderot--Paris 7, Sorbonne Paris Cité, UMR 7586, Institut de Mathématiques de Jussieu--PRG, Case 7012, F-75013 Paris, France. Email address: regis.delabreteche@imj-prg.fr
Institut Élie Cartan, Université de Lorraine, BP 70239, F-54506 Vandoeuvre-lès-Nancy Cedex, France. Email address: gerald.tenenbaum@univ-lorraine.fr

References

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Sur les processus arithmétiques liés aux diviseurs

  • R. de la Bretèche (a1) and G. Tenenbaum (a2)

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