Sur une application de la formule de Selberg-Delange

F. Ben Saïd; J.-L. Nicolas

Colloquium Mathematicae (2003)

  • Volume: 98, Issue: 2, page 223-247
  • ISSN: 0010-1354

Abstract

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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) ( w h e r e i = 0 o r 1 ) , a n d m ≡ l ( m o d b ) . The above quantity has appeared in the paper [3] to estimate the number of elements up to x of the set of positive integers containing 1, 2 and 3 and such that the number p(,n) of partitions of n with parts in is even, for all n ≥ 4.

How to cite

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F. Ben Saïd, and J.-L. Nicolas. "Sur une application de la formule de Selberg-Delange." Colloquium Mathematicae 98.2 (2003): 223-247. <http://eudml.org/doc/284796>.

@article{F2003,
author = {F. Ben Saïd, J.-L. Nicolas},
journal = {Colloquium Mathematicae},
keywords = {Selberg-Delange formula; sums over integers in a restricted set},
language = {fre},
number = {2},
pages = {223-247},
title = {Sur une application de la formule de Selberg-Delange},
url = {http://eudml.org/doc/284796},
volume = {98},
year = {2003},
}

TY - JOUR
AU - F. Ben Saïd
AU - J.-L. Nicolas
TI - Sur une application de la formule de Selberg-Delange
JO - Colloquium Mathematicae
PY - 2003
VL - 98
IS - 2
SP - 223
EP - 247
LA - fre
KW - Selberg-Delange formula; sums over integers in a restricted set
UR - http://eudml.org/doc/284796
ER -

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