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math.NT2026
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 funct…
math.NT2026
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 bet…
math.NT2026
On a Smoothed Dirichlet Divisor Problem
Olivier Bordellès, Florian Daval
Hardy showed that $\sum_{n \ioe x}τ(n)-x(\log x +2γ-1)$ is not . In this article, we prove that $\sum_{n \ioe x}τ(n)(1-\frac{x}{n})-xP(\log x)=\frac{1}{4}+O \left( \fra…