11 citations · 14 across the 7 of their papers we have counts for
7 papers
The large sieve through Parseval, Large sifted sets are regular
Olivier Ramaré
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, we prov…
Improving on the Brun-Titchmarsh Theorem
Olvier Ramaré, Jan Christoph Schlage-Puchta
We prove that the number of primes in an interval of length is at most when is large enough. This is obtained through a sieving process which can be seen…
The trigonometric polynomial on sums of two squares, an additive problem and generalisation
Olivier Ramare, GK Viswanadham
Let be the set of odd integers that are sums of two coprime squares. We prove that the trigonometric polynomial satisfies \[ \frac{S(α; N)}…
An explicit upper bound for when is quadratic
D. R. Johnston, O. Ramare, T. S. Trudgian
We consider Dirichlet -functions where is a non-principal quadratic character to the modulus . We make explicit a result due to Pintz and Stephens by showing th…
A higher order Levin-Feinleib theorem
Olivier Ramare, Alisa Sedunova, Ritika Sharma
When restricted to some non-negative multiplicative function, say f, bounded on primes and that vanishes on non square-free integers, our result provides us with an asymptotic for…
On the behaviour of $γ\Log p$ modulo 1
Olivier Ramaré
We prove non-trivial lower bounds for sums of type $\sum_{p\sim P}g(γ\Log p)$, where is a non-negative -periodical function and is a given parameter. As an application…
The number of rational numbers determined by large sets of integers
Javier Cilleruelo, D. S. Ramana, Olivier Ramare
When and are subsets of the integers in and respectively, with and , we show that the number of rational numbers expressible as $…