Publications by Pierre Francis André Le Boudec

On the distribution of squarefree integers in arithmetic progressions

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, we prove an upper bound for its variance as a varies over (Z/qZ)(x) which consid ...

SPRINGER HEIDELBERG2018

Height of rational points on quadratic twists of a given elliptic curve

Pierre Francis André 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 varies. This conjecture seems to be very deep and we can prove only partial resul ...

Oxford Univ Press2016

Density of Rational Points on a Certain Smooth Bihomogeneous Threefold

Pierre Francis André 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). These bounds are in agreement with Manin's conjecture. ...

Oxford University Press2015

Linear Growth for Certain Elliptic Fibrations

Pierre Francis André 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. ...

Oxford University Press2015

Affine congruences and rational points on a certain cubic surface

Pierre Francis André 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 whose singularity type is D-4. This improves on a result of Browning and answers a ...

Mathematical Science Publ2014