O. Ramar'e

activity

20082025

most citedConvolution of periodic multiplicative functions and the divisor problem

1 citations · 1 across the 9 of their papers we have counts for

collaborators

Showing 2023 · math.NTShow all

4 papers · 2 filters

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 $X \geq 2$ .

math.NT2023★ 1 cited

Convolution of periodic multiplicative functions and the divisor problem

Marco Aymone, Gopal Maiti, Olivier Ramaré +1

We study a certain class of arithmetic functions that appeared in Klurman's classification of $\pm 1$ multiplicative functions with bounded partial sums, c.f., Comp. Math. 153 (8),…

math.NT2023

A spectral resolution of the large sieve

Olivier Ramaré

The quadratic form $V (φ, Q) = \sum_{q \sim Q} \sum_{a mod^{*} q} ∣ S (φ, a / q) ∣^{2}$ and its eigenvalues are well understood when $Q = o (N)$ , while $V (φ, Q)$ is expected to behave like a Rie…