Sur les processus arithmétiques liés aux diviseurs
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 proces...
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| Veröffentlicht in: | Advances in applied probability 2016-07, Vol.48 (A), p.63-76 |
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| container_title | Advances in applied probability |
| container_volume | 48 |
| creator | de la Bretèche, R. Tenenbaum, G. |
| description | 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
). |
| doi_str_mv | 10.1017/apr.2016.42 |
| format | Article |
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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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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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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
).</abstract><cop>Cambridge, UK</cop><pub>Cambridge University Press</pub><doi>10.1017/apr.2016.42</doi><tpages>14</tpages><oa>free_for_read</oa></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0001-8678 |
| ispartof | Advances in applied probability, 2016-07, Vol.48 (A), p.63-76 |
| issn | 0001-8678 1475-6064 |
| language | eng |
| recordid | cdi_crossref_primary_10_1017_apr_2016_42 |
| source | Cambridge Journals; JSTOR Mathematics & Statistics; JSTOR Archive Collection A-Z Listing |
| title | Sur les processus arithmétiques liés aux diviseurs |
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