Related papers: Integral points of bounded height on quintic del P…

We characterise integral points of bounded log-anticanonical height on a quartic del Pezzo surface of singularity type $\mathbf{A}_3$ over imaginary quadratic fields with respect to its singularity and its lines. Furthermore, we count these…

We prove an asymptotic formula for the number of integral points of bounded log anticanonical height on a singular quartic del Pezzo surface over arbitrary number fields, with respect to the largest admissible boundary divisor. The…

In order to study integral points of bounded log-anticanonical height on weak del Pezzo surfaces, we classify weak del Pezzo pairs. As a representative example, we consider a quartic del Pezzo surface of singularity type…

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

We prove Manin's conjecture for split smooth quintic del Pezzo surfaces over arbitrary number fields with respect to fairly general anticanonical height functions. After passing to universal torsors, we first show that we may restrict the…

We establish asymptotic formulas for the number of integral points of bounded height on toric varieties.

An asymptotic formula is established for the number of rational points of bounded height on a non-singular quartic del Pezzo surface with a conic bundle structure.

We establish asymptotic formulas for the number of integral points of bounded height on partial equivariant compactifications of vector groups.

We give upper bounds for the number of rational points of bounded anti-canonical height on del Pezzo surfaces of degree at most five over any global field whose characteristic is not equal to two or three. For number fields these results…

In this article, we obtain an upper bound for the number of integral points on the del Pezzo surfaces of degree two.

We determine an asymptotic formula for the number of integral points of bounded height on a blow-up of $\mathbb{P}^3$ outside certain planes using universal torsors.

Upper and lower bounds, of the expected order of magnitude, are obtained for the number of rational points of bounded height on any quartic del Pezzo surface over $\mathbb{Q}$ that contains a conic defined over $\mathbb{Q}$.

Manin's conjecture for the asymptotic behavior of the number of rational points of bounded height on del Pezzo surfaces can be approached through universal torsors. We prove several auxiliary results for the estimation of the number of…

We prove asymptotic formulas for the number of rational points of bounded height on certain equivariant compactifications of the affine plane.

For any number field k, upper bounds are established for the number of k-rational points of bounded height on non-singular del Pezzo surfaces defined over k, which are equipped with suitable conic bundle structures over k.

We study the asymptotic distribution of integral points of bounded height on partial bi-equivariant compactifications of semi-simple groups of adjoint type.

In the paper we partially solved the problem of the distribution of the discriminants of integral polynomials in the cubic case. We proved the asymptotic formula for the number of integral cubic polynomials having bounded height and bounded…

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 way, we investigate the average number of integral points…

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

We extend work of Heath-Brown and Salberger, based on the determinant method, to provide a uniform upper bound for the number of integral points of bounded height on an affine surface, which are subject to a polynomial congruence condition.…