O. Ramar'e

activity

20082025

collaborators

Showing 2024Show all

3 papers · 1 filter

math.NT2024

Cusps of primes in dense subsequences -- Bypassing the $W$ -trick

Olivier Ramaré

Let the $A$ -cusps of a dense subset $P^{*} \in [N, N]$ of primes be points $α \in R / Z$ that are such that $|\sum_{\substack{p\in\mathcal{P}^*}} e(αp)|\g…

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…

Cusps of primes in dense subsequences -- Bypassing the W-trick

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

An L2-bound for the Barban-Vehov weights

Cusps of primes in dense subsequences -- Bypassing the $W$ -trick

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