S. Z. Alterman

collaborators

4 papers

math.NT2026

On a MÃ¶bius double sum

Olivier RamarÃ©, Sebastian Zuniga Alterman

We study the double sum $S_{ε} (X)$ $=$ $\sum_{d, e \leq X} \frac{I ^ ¼ ( d ) I ^ ¼ ( e )}{[ d , e ] ^{1 + ε}}$ , which converges even in the case $ε = 0$ , where $I^¼$ deno…

math.NT2026

MÃ¶bius function and primes: an identity factory with applications

Olivier RamarÃ©, Sebastian Zuniga Alterman

We investigate the sums $\sum_{n \leq X, (n, q) = 1} \frac{I ^ ¼ ( n )}{n ^{s}} lo g^{k} (\frac{X}{n})$ , where $k \in {0, 1}$ , $s \in C$ , $ℜ s > 0$ . Our goal is to obtain explicit as…

math.NT2024

From explicit estimates for the primes to explicit estimates for the MÃ¶bius function II

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}Î¼(n)\B…

math.NT2024

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

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

On a MÃ¶bius double sum

MÃ¶bius function and primes: an identity factory with applications

From explicit estimates for the primes to explicit estimates for the MÃ¶bius function II

An L2-bound for the Barban-Vehov weights

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