O. Ramar'e

activity

20242026

collaborators

3 papers

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.NT2025

Rudin Inequality, Chang Theorem, primes and squares

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

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

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

Rudin Inequality, Chang Theorem, primes and squares

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

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