Some elementary explicit bounds for two mollifications of the Moebius function

Ramaré, Olivier

Document type :

Compte-rendu et recension critique d'ouvrage

DOI :

10.7169/facm/2013.49.2.3

Title :

Some elementary explicit bounds for two mollifications of the Moebius function

Author(s) :

Ramaré, Olivier [Auteur]
Centre National de la Recherche Scientifique [CNRS]
Laboratoire Paul Painlevé - UMR 8524 [LPP]

Journal title :

Functiones et Approximatio Commentarii Mathematici

Pages :

229-240

Publisher :

Poznań : Wydawnictwo Naukowe Uniwersytet im. Adama Mickiewicza

Publication date :

2013-12

ISSN :

0208-6573

HAL domain(s) :

Mathématiques [math]/Théorie des nombres [math.NT]

English abstract : [en]

We prove that the $\sum_{d\le x, (d,r)=1}\mu(d)/d^{1+\varepsilon}$ is bounded by $1 + \varepsilon$, uniformly in $x \ge 1$, $r$ and $\varepsilon > 0$. We prove a similar estimate for the quantity $\sum_{d\le x, (d,r)=1} ...
Show more >We prove that the $\sum_{d\le x, (d,r)=1}\mu(d)/d^{1+\varepsilon}$ is bounded by $1 + \varepsilon$, uniformly in $x \ge 1$, $r$ and $\varepsilon > 0$. We prove a similar estimate for the quantity $\sum_{d\le x, (d,r)=1} \mu(d) \log(x/d)/d^{1+\varepsilon}. When $\varepsilon=0$, $r$ r varies between 1 and a hundred, and x is below a million, this sum is non-negative and this raises the question as to whether it is non-negative for every x.Show less >

Language :

Anglais

Popular science :

Non

Collections :

Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL

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