Sur une application de la formule de Selberg-Delange

• Autorzy: F. Ben Saïd , J.-L. Nicolas
• Języki publikacji: FR EN

Abstrakty

EN

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 $2^{ω(m)}m ≤ x$, all prime factors of m are congruent to 3, 5 or 6 modulo 7, Ω(m) ≡ i (mod 2)$ (where i = 0 or 1), and m ≡ l (mod b).
The above quantity has appeared in the paper [3] to estimate the number of elements up to x of the set 𝓐 of positive integers containing 1, 2 and 3 and such that the number p(𝓐,n) of partitions of n with parts in 𝓐 is even, for all n ≥ 4.

Kategorie tematyczne

• 11N37: Asymptotic results on arithmetic functions
• 11N25: Distribution of integers with specified multiplicative constraints

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2003
• Tom: 98
• Numer: 2
• Strony: 223-247

Daty

wydano

2003

Twórcy

autor

F. Ben Saïd

• Faculté des Sciences de Monastir, Avenue de l'environnement, 5000, Monastir, Tunisie

autor

J.-L. Nicolas

• Institut Girard Desargues, UMR 5028, Bât. Doyen Jean Braconnier, Université Claude Bernard (Lyon 1), 21 Avenue Claude Bernard, F-69622 Villeurbanne Cedex, France

Identyfikatory

DOI

10.4064/cm98-2-8