S. Z. Alterman

collaborators

3 papers

math.NT2026

On a Möbius double sum

Olivier Ramaré, Sebastian Zuniga Alterman

We study the double sum $S_{ε} (X)$ $=$ $\sum_{d, e \leq X} \frac{μ ( d ) μ ( e )}{[ d , e ] ^{1 + ε}}$ , which converges even in the case $ε = 0$ , where $μ$ denotes…

math.NT2024

From explicit estimates for the primes to explicit estimates for the Möbius function II

Olivier Ramaré, Sebastian Zuniga Alterman

We improve on all the results of [13] by incorporating the finite range computations performed since then by several authors. Thus we have \begin{align*} \Bigg|\sum_{n\le X}μ(n)\Bi…

math.NT2024

An $L^{2}$ -bound for the Barban-Vehov weights

Olivier Ramaré, Sebastian Zuniga Alterman

Let $λ$ the Barban--Vehov weights, defined in $(1)$ . Let $X \geq z_{1} \geq 100$ and $z_{2} = z_{1}^{τ}$ for some $τ > 1$ . We prove that \begin{equation*} \sum_{n\le X}\frac{1}{n}\Bigl(\sum_{\subst…

On a Möbius double sum

From explicit estimates for the primes to explicit estimates for the Möbius function II

An L2-bound for the Barban-Vehov weights

An $L^{2}$ -bound for the Barban-Vehov weights