Efthymios Sofos

Rational points of bounded height on general conic bundle surfaces

A conjecture of Manin predicts the asymptotic distribution of rational points of bounded height on Fano varieties. In this paper we use conic bundles to obtain correct lower bounds for a wide class of surfaces over number fields for which the conjecture is still far from being proved. For example, we obtain the conjectured lower bound of Manins conjecture for any del Pezzo surface whose Picard rank is sufficiently large, or for arbitrary del Pezzo surfaces after possibly an extension of the ground field of small degree.

Uniformly counting rational points on conics

We provide an asymptotic estimate for the number of rational points of bounded height on a non-singular conic over Q. The estimate is uniform in the coefficients of the underlying quadratic form.

Serre's problem on the density of isotropic fibres in conic bundles

Let

Counting rational points on quartic del Pezzo surfaces with a rational conic

\pi:X\to \mathbb{P}^1_{\mathbb{Q}}

GENERALISED DIVISOR SUMS OF BINARY FORMS OVER NUMBER FIELDS

be a non-singular conic bundle over

Finite Saturation for Unirational Varieties

\mathbb{Q}

On the distribution of the density of maximal order elements in general linear groups

having

Counting rational points on smooth cubic surfaces

n

SARNAK’S SATURATION PROBLEM FOR COMPLETE INTERSECTIONS

non-split fibres and denote by

Averages of Arithmetic Functions over Principal Ideals

N(\pi,B)