La lecture à portée de main
Découvre YouScribe en t'inscrivant gratuitement
Je m'inscrisDécouvre YouScribe en t'inscrivant gratuitement
Je m'inscrisDescription
Sujets
Informations
Publié par | profil-urra-2012 |
Nombre de lectures | 11 |
Langue | English |
Extrait
1
Some elementary explicit bounds for two
mollifications of the Moebius function
O.Ramar´
March 8, 2012
Abstract
P
1+ε
We prove that the sumµ(d)/dis bounded by 1+ε,
d≤x,
(d,r)=1
uniformly inx≥1,randε >prove a similar estimate for the0. We
P
1+ε
quantityµ(d) Log(x/d)/d. Whenε= 0,rvaries between
d≤x,
(d,r)=1
1 and a hundred, andxis below a million, this sum is non-negative and
this raises the question as to whether it is non-negativefor everyx.
Introduction and results
Our first result is the following:
Theorem 1.1.Whenr≥1andε≥0, we have
X
µ(d)
≤1 +ε.