Improving on some results of J.-L. Nicolas [15], the elements of the set , for which the partition function (i.e. the number of partitions of with parts in ) is even for all are determined. An asymptotic estimate to the counting function of this set is also given.
Dans cet article, nous complétons les résultats de J.-L. Nicolas [15], en déterminant tous les éléments de l’ensemble pour lequel la fonction de partition (c-à-d le nombre de partitions de en parts dans ) est paire pour tout . Nous donnons aussi un équivalent asymptotique à la fonction de décompte de cet ensemble.
Mots-clés : Partitions, periodic sequences, order of a polynomial, orbits, $2$-adic numbers, counting function, Selberg-Delange formula.
@article{JTNB_2010__22_1_51_0,
author = {Ben Sa{\"\i}d, Fethi and Nicolas, Jean-Louis and Zekraoui, Ahlem},
title = {On the parity of generalized partition {functions,~III}},
journal = {Journal de th\'eorie des nombres de Bordeaux},
pages = {51--78},
publisher = {Universit\'e Bordeaux 1},
volume = {22},
number = {1},
year = {2010},
doi = {10.5802/jtnb.704},
zbl = {1236.11088},
mrnumber = {2675873},
language = {en},
url = {http://archive.numdam.org/articles/10.5802/jtnb.704/}
}
TY - JOUR AU - Ben Saïd, Fethi AU - Nicolas, Jean-Louis AU - Zekraoui, Ahlem TI - On the parity of generalized partition functions, III JO - Journal de théorie des nombres de Bordeaux PY - 2010 SP - 51 EP - 78 VL - 22 IS - 1 PB - Université Bordeaux 1 UR - http://archive.numdam.org/articles/10.5802/jtnb.704/ DO - 10.5802/jtnb.704 LA - en ID - JTNB_2010__22_1_51_0 ER -
%0 Journal Article %A Ben Saïd, Fethi %A Nicolas, Jean-Louis %A Zekraoui, Ahlem %T On the parity of generalized partition functions, III %J Journal de théorie des nombres de Bordeaux %D 2010 %P 51-78 %V 22 %N 1 %I Université Bordeaux 1 %U http://archive.numdam.org/articles/10.5802/jtnb.704/ %R 10.5802/jtnb.704 %G en %F JTNB_2010__22_1_51_0
Ben Saïd, Fethi; Nicolas, Jean-Louis; Zekraoui, Ahlem. On the parity of generalized partition functions, III. Journal de théorie des nombres de Bordeaux, Volume 22 (2010) no. 1, pp. 51-78. doi : 10.5802/jtnb.704. http://archive.numdam.org/articles/10.5802/jtnb.704/
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