4 papers
On a Smoothed Walfisz Divisor Problem
Olivier Bordellès, Florian Daval
This work is in the spirit of our previous investigation on a smooth Dirichlet divisor problem, where we now replace the Dirichlet divisor function by the sum-of-divisors func…
On a Smoothed Dirichlet Divisor Problem
Olivier Bordellès, Florian Daval
Hardy showed that $\sum_{n \ioe x}Ï(n)-x(\log x +2γ-1)$ is not . In this article, we prove that $\sum_{n \ioe x}Ï(n)(1-\frac{x}{n})-xP(\log x)=\frac{1}{4}+O \left( \…
A note on the -adic valuation of
Olivier Bordellès
In this note, we obtain an exact formula for the -adic valuation of where is an odd prime, allowing us to derive an explicit upper bound which is asymptotically be…
An explicit result for short sums of positive arithmetic functions
Olivier Bordellès
We prove a totally explicit bound for short sums of certain non-negative arithmetic functions satisfying a general growth condition, and apply this result to derive two explicit es…