10 citations · 29 across the 6 of their papers we have counts for
6 papers
On the distribution of squarefree integers in arithmetic progressions
Pierre Le Boudec
We investigate the error term of the asymptotic formula for the number of squarefree integers up to some bound, and lying in some arithmetic progression a (mod q). In particular, w…
Height of rational points on quadratic twists of a given elliptic curve
Pierre Le Boudec
We formulate a conjecture about the distribution of the canonical height of the lowest non-torsion rational point on a quadratic twist of a given elliptic curve, as the twist varie…
Density of rational points on a certain smooth bihomogeneous threefold
Pierre Le Boudec
We establish sharp upper and lower bounds for the number of rational points of bounded anticanonical height on a smooth bihomogeneous threefold defined over Q and of bidegree (1, 2…
Affine congruences and rational points on a certain cubic surface
Pierre Le Boudec
We establish estimates for the number of solutions of certain affine congruences. These estimates are then used to prove Manin's conjecture for a cubic surface split over Q and who…
Manin's conjecture for a cubic surface with 2A_2+A_1 singularity type
Pierre Le Boudec
We establish Manin's conjecture for a cubic surface split over Q and whose singularity type is 2A_2+A_1. For this, we make use of a deep result about the equidistribution of the va…
Manin's conjecture for a quartic del Pezzo surface with A_3 singularity and four lines
Pierre Le Boudec
We establish Manin's conjecture for a quartic del Pezzo surface split over Q and having a singularity of type A_3 and containing exactly four lines. It is the first example of spli…