3 citations · 5 across the 7 of their papers we have counts for
6 papers · 1 filter
Ranks of elliptic curves over of small degree in
Francesco Battistoni, Sandro Bettin, Christophe Delaunay
We study elliptic surfaces over with coefficients of a Weierstrass model being polynomials in with degree at most 2. We derive an explicit expressio…
On the typical rank of elliptic curves over
Francesco Battistoni, Sandro Bettin, Christophe Delaunay
We give upper bounds for the number of rational elliptic surfaces in some families having positive rank, obtaining in particular that these form a subset of density zero. This conf…
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…
The Cohen-Lenstra heuristics, moments and -ranks of some groups
Christophe Delaunay, Frédéric Jouhet
This article deals with the coherence of the model given by the Cohen-Lenstra heuristic philosophy for class groups and also for their generalizations to Tate-Shafarevich groups. M…
Zero free regions for Dirichlet series
Christophe Delaunay, Emmanuel Fricain, Elie Mosaki +1
In this paper, we are interested in explicit zero-free discs for some Dirichlet series and we also study a general Beurling-Nyman criterion for -functions. Our results generaliz…
Regulators of rank one quadratic twists
Christophe Delaunay, Xavier-François Roblot
We investigate the regulators of elliptic curves with rank 1 in some families of quadratic twists of a fixed elliptic curve. In particular, we formulate some conjectures on the ave…