49 citations · 178 across the 28 of their papers we have counts for
5 papers · 1 filter
Non-isotrivial elliptic surfaces with non-zero average root number
Sandro Bettin, Chantal David, Christophe Delaunay
We consider the problem of finding -parameter families of elliptic curves whose root number does not average to zero as the parameter varies in . We classify all suc…
A quadratic divisor problem and moments of the Riemann zeta-function
Sandro Bettin, H. M. Bui, Xiannan Li +1
We estimate asymptotically the fourth moment of the Riemann zeta-function twisted by a Dirichlet polynomial of length . Our work relies crucially on Watt…
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 first moment of twisted Hecke -functions with unbounded shifts
Sandro Bettin
We compute the first moment of twisted Hecke -functions of prime power level going to infinity, uniformly in the conductor of the twist and in the vertical shift.
The conjecture implies the Riemann hypothesis
Sandro Bettin, Steven M. Gonek
We show that the conjecture implies the Riemann hypothesis.