24 citations · 25 across the 4 of their papers we have counts for
4 papers
A weighted one-level density of the non-trivial zeros of the Riemann zeta-function
Sandro Bettin, Alessandro Fazzari
We compute the one-level density of the non-trivial zeros of the Riemann zeta-function weighted by for and, for test functions with Fourier support in…
A congruence sum and rational approximations
Sandro Bettin
We give a reciprocity formula for a two-variable sum where the variables satisfy a linear congruence condition. We also prove that such sum is a measure of how well a rational is a…
On the reciprocity law for the twisted second moment of Dirichlet -functions
Sandro Bettin
We investigate the reciprocity law, studied by Conrey~\cite{Con07} and Young~\cite{You11a}, for the second moment of Dirichlet L-functions twisted by modulo a prime . We…
The mean square of the product of with Dirichlet polynomials
Sandro Bettin, Vorrapan Chandee, Maksym Radziwill
Improving earlier work of Balasubramanian, Conrey and Heath-Brown, we obtain an asymptotic formula for the mean-square of the Riemann zeta-function times an arbitrary Dirichlet pol…