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Currently displaying 1 – 4 of 4

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Even partition functions.

Ben Saïd, F.; Nicolas, J.-L. — 2002

Séminaire Lotharingien de Combinatoire [electronic only]

Sets of parts such that the partition function is even

Ben Saïd; J.-N. Nicolas — 2003

Acta Arithmetica

Sur une application de la formule de Selberg-Delange

F. Ben Saïd; J.-L. Nicolas — 2003

Colloquium Mathematicae

E. Landau has given an asymptotic estimate for the number of integers up to x whose prime factors all belong to some arithmetic progressions. In this paper, by using the Selberg-Delange formula, we evaluate the number of elements of somewhat more complicated sets. For instance, if ω(m) (resp. Ω(m)) denotes the number of prime factors of m without multiplicity (resp. with multiplicity), we give an asymptotic estimate as x → ∞ of the number of integers m satisfying $2^{ω (m)} m \leq x$ , all prime factors of m are congruent...

On the parity of generalized partition functions, III

Fethi Ben Saïd; Jean-Louis Nicolas; Ahlem Zekraoui — 2010

Journal de Théorie des Nombres de Bordeaux

Improving on some results of J.-L. Nicolas [], 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 $n \geq 6$ are determined. An asymptotic estimate to the counting function of this set is also given.

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