Related papers: On Manin's conjecture for Ch\^atelet surfaces

The Manin conjecture is established for Ch\^atelet surfaces over Q arising as minimal proper smooth models of the surface Y^2+Z^2=f(X) where f is a totally reducible polynomial of degree 3 without repeated roots. These surfaces do not…

Following the line of attack from La Bret\`eche, Browning and Peyre, we prove Manin's conjecture in its strong form conjectured by Peyre for a family of Ch\^atelet surfaces which are defined as minimal proper smooth models of affine…

We prove Manin's conjecture over imaginary quadratic number fields for a cubic surface with a singularity of type E_6.

In this paper, we prove a conjecture of Schnell in the surface case.

We prove that any smooth cubic surface defined over any number field satisfies the lower bound predicted by Manin's conjecture possibly after an extension of small degree.

We give a relatively short and elementary proof of Manin's conjecture for split smooth quintic del Pezzo surfaces over the rational numbers.

Manin's conjecture is proved for a split del Pezzo surface of degree 5 with a singularity of type A_2.

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 split singular quartic del Pezzo surface whose universal torsor…

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 values of a certain restricted divisor function in three…

The representation of integral binary forms as sums of two squares is discussed and applied to establish the Manin conjecture for certain Ch\^atelet surfaces defined over the rationals.

Given a nonsingular quartic del Pezzo surface, a conjecture of Manin predicts the density of rational points on the open subset of the surface formed by deleting the lines. We prove that this prediction is of the correct order of magnitude…

We investigate Manin's conjecture for del Pezzo surfaces of degree five with a conic bundle structure, proving matching upper and lower bounds, and the full conjecture in the Galois general case.

The Manin conjecture is established for a split singular cubic surface in P^3, with singularity type D_5.

The Manin conjecture is established for a split singular del Pezzo surface of degree four, with singularity type A_4.

Artin's conjecture is established for all forms that can be realised as a diagonal form on an hyperplane.

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 whose singularity type is D_4. This improves on a result of…

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 certain restricted divisor function and use a result about the…

We show, conditionally on Schinzel's hypothesis, that the only obstruction to the integral Hasse principle for generalised affine Ch\^{a}telet surfaces is the Brauer--Manin one.

We prove a lower bound that agrees with Manin's prediction for the number of rational points of bounded height on the Fermat cubic surface. As an application we provide a simple counterexample to Manin's conjecture over the rationals.

We prove effective versions of algebraic and analytic Lang's conjectures for product-quotient surfaces of general type with $P_g=0$ and $c_1^2=c_2$.