On the parity of generalized partition functions, III
Journal de théorie des nombres de Bordeaux, Tome 22 (2010) no. 1, pp. 51-78.

Dans cet article, nous complétons les résultats de J.-L. Nicolas [15], en déterminant tous les éléments de l’ensemble 𝒜=𝒜(1+z+z 3 +z 4 +z 5 ) pour lequel la fonction de partition p(𝒜,n) (c-à-d le nombre de partitions de n en parts dans 𝒜) est paire pour tout n6. Nous donnons aussi un équivalent asymptotique à la fonction de décompte de cet ensemble.

Improving on some results of J.-L. Nicolas [15], the elements of the set 𝒜=𝒜(1+z+z 3 +z 4 +z 5 ), for which the partition function p(𝒜,n) (i.e. the number of partitions of n with parts in 𝒜) is even for all n6 are determined. An asymptotic estimate to the counting function of this set is also given.

DOI : 10.5802/jtnb.704
Classification : 11P81, 11N25, 11N37
Mots clés : Partitions, periodic sequences, order of a polynomial, orbits, $2$-adic numbers, counting function, Selberg-Delange formula.
Ben Saïd, Fethi 1 ; Nicolas, Jean-Louis 2 ; Zekraoui, Ahlem 1

1 Université de Monastir Faculté des Sciences de Monastir Avenue de l’Environement 5000 Monastir, Tunisie
2 Université de Lyon 1 Institut Camile Jordan, UMR 5208 Batiment Doyen Jean Braconnier 21 Avenue Claude Bernard F-69622 Villeurbanne, France
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Ben Saïd, Fethi; Nicolas, Jean-Louis; Zekraoui, Ahlem. On the parity of generalized partition functions, III. Journal de théorie des nombres de Bordeaux, Tome 22 (2010) no. 1, pp. 51-78. doi : 10.5802/jtnb.704. http://www.numdam.org/articles/10.5802/jtnb.704/

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