In this paper, we introduce a certain combinatorial
property $Z^\star(k)$, which is defined for every integer $k\ge 2$,
and show that every set $E\subset\Z$ with the property $Z^\star(k)$
is necessarily a noncommutative $\Lambda(2k)$ set. In particular,
using number theoretic results about the number of solutions to
so-called ``$S$-unit equations,'' we show that for any finite set $Q$
of prime numbers the set $E_Q$ of natural numbers whose prime divisors
all lie in the set $Q$ is noncommutative $\Lambda(p)$ for every real
number $2
Publié le : 2003-10-15
Classification:
46L52,
11N25,
43A46,
47B10
@article{1258138091,
author = {Banks, William D. and Harcharras, Asma},
title = {New examples of noncommutative $\L ambda(p)$ sets},
journal = {Illinois J. Math.},
volume = {47},
number = {4},
year = {2003},
pages = { 1063-1078},
language = {en},
url = {http://dml.mathdoc.fr/item/1258138091}
}
Banks, William D.; Harcharras, Asma. New examples of noncommutative $Łambda(p)$ sets. Illinois J. Math., Tome 47 (2003) no. 4, pp. 1063-1078. http://gdmltest.u-ga.fr/item/1258138091/