On the joint distribution of q-additive functions on polynomial sequences

Steiner, Wolfgang

Steiner, Wolfgang

HAL, hal-00023222 / Harvested from HAL

Text on HAL

Résumé

The joint distribution of sequences

$(f_\ell(P_\ell(n)))_{n\in\Bbb N},\ell=1,2,\dots,d$ and

$(f_\ell(P_\ell(p)))_{p\in\Bbb P}$ respectively, where

$f_\ell$ are

$q_\ell$ -additive functions and

$P_\ell$ polynomials with integer coefficients, is considered. A central limit theorem is proved for a larger class of

$q_\ell$ and

$P_\ell$ than by Drmota~[3]. In particular, the joint limit distribution of the sum-of-digits functions

$s_{q_1}(n),s_{q_2}(n)$ is obtained for arbitrary integers

$q_1,q_2$ . For strongly

$q$ -additive functions with respect to the same

$q$ , a central limit theorem is proved for arbitrary polynomials

$P_\ell$ with the help of a joint representation of the digits of

$P_\ell(n)$ by a Markov chain.

Publié le : 2002-07-05
Classification: somme des chiffres, théorème central limite, chaîne de Markov, 11N60, 60J10, [MATH.MATH-NT]Mathematics [math]/Number Theory [math.NT]

@article{hal-00023222,
     author = {Steiner, Wolfgang},
     title = {On the joint distribution of q-additive functions on polynomial sequences},
     journal = {HAL},
     volume = {2002},
     number = {0},
     year = {2002},
     language = {en},
     url = {http://dml.mathdoc.fr/item/hal-00023222}
}

Steiner, Wolfgang. On the joint distribution of q-additive functions on polynomial sequences. HAL, Tome 2002 (2002) no. 0, . http://gdmltest.u-ga.fr/item/hal-00023222/