1 citations · 2 across the 4 of their papers we have counts for
5 papers · 1 filter
The Hasse principle for random Fano hypersurfaces
Tim Browning, Pierre Le Boudec, Will Sawin
It is known that the Brauer--Manin obstruction to the Hasse principle is vacuous for smooth Fano hypersurfaces of dimension at least over any number field. Moreover, for such v…
Height of rational points on random Fano hypersurfaces
Pierre Le Boudec
We investigate in a statistical fashion the smallest height of a rational point on a Fano hypersurface defined over the field of rational numbers. Along the way, we establish an av…
A statistical view on the conjecture of Lang about the canonical height on elliptic curves
Pierre Le Boudec
We adopt a statistical point of view on the conjecture of Lang which predicts a lower bound for the canonical height of non-torsion rational points on elliptic curves defined over…
Height of rational points on congruent number elliptic curves
Pierre Le Boudec
We prove that a positive proportion of squarefree integers are congruent numbers such that the canonical height of the lowest non-torsion rational point on the corresponding ellipt…
Average rank in families of quadratic twists: a geometric point of view
Pierre Le Boudec
We investigate the average rank in the family of quadratic twists of a given elliptic curve defined over , when the curves are ordered using the canonical height of the…