2 citations · 4 across the 9 of their papers we have counts for
9 papers
Arithmetic dynamics of random polynomials
Pierre Le Boudec, Niki Myrto Mavraki
We investigate from a statistical perspective the arithmetic properties of the dynamics of polynomials of fixed degree and defined over the field of rational numbers. To start with…
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…
Integral points on quadratic twists and linear growth for certain elliptic fibrations
Pierre Le Boudec
We prove that the number of rational points of bounded height on certain del Pezzo surfaces of degree 1 defined over Q grows linearly, as predicted by Manin's conjecture. Along the…
Power-free values of the polynomial t_1...t_r - 1
Pierre Le Boudec
Let k, r > 1 be two integers. We prove an asymptotic formula for the number of k-free values of the r variables polynomial t_1...t_r - 1 over the integral points of [1, x]^r.
Manin's conjecture for two quartic del Pezzo surfaces with 3A_1 and A_1+A_2 singularity types
Pierre Le Boudec
We prove Manin's conjecture for two del Pezzo surfaces of degree four which are split over Q and whose singularity types are respectively 3A_1 and A_1+A_2. For this, we study a cer…