O. Ramar'e

activity

20082025

most citedCounting ideals in ray classes

3 citations · 4 across the 14 of their papers we have counts for

collaborators

19 papers

math.NT2025

Rudin Inequality, Chang Theorem, primes and squares

Olivier Ramaré

We prove that the set of large values of the trigonometric polynomial over a subset of density of the primes has some additive structure, similarly to what happens for subsets of d…

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…

math.NT2023

Möbius function and primes: an identity factory with applications

Olivier Ramaré, Sebastian Zuniga Alterman

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

math.NT2023

A Moebius sum

Olivier Ramaré

We provide numerical bounds for $Σ (X) = \sum_{d_{1}, d_{2} \leq X} \frac{μ ( d _{1} ) μ ( d _{2} )}{[ d _{1} , d _{2} ]}$ . We show in particular that $0 \leq Σ (X) \leq 17/25$ for every $X \geq 2$ .

Rudin Inequality, Chang Theorem, primes and squares

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

Möbius function and primes: an identity factory with applications

A Moebius sum

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

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