Olivier Ramar'e

collaborators

3 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

The weighted large sieve through Parseval

Olivier RamarÃ©

We modify the approach to the arithmetical form of the large sieve by relying on the Parseval identity rather than on an approximate Bessel inequality and as a consequence, improve…

math.NT2026

Bounding the exponential sum on squares of some sifted sequences

Let $B$ denote the collection of odd primitive Gaussian integers and $n \mapsto b (n)$ denote the characteristic function of elements of $B$ . We prove that the…