Related papers: Integral points of bounded height on toric varieti…

We determine an asymptotic formula for the number of integral points of bounded height on a certain toric variety, which is incompatible with part of a preprint by Chambert-Loir and Tschinkel. We provide an alternative interpretation of the…

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

We combine the split torsor method and the hyperbola method for toric varieties to count rational points and Campana points of bounded height on certain subvarieties of toric varieties.

We establish an asymptotic formula for the number of $\mathcal{M}$-points of bounded height on split toric varieties, for the height induced by any big and nef divisor class. This formula establishes new cases of the extension of Manin's…

We prove asymptotics for semi-integral points of bounded height on toric varieties. We verify the Manin-type conjecture of Pieropan, Smeets, Tanimoto and V\'arilly-Alvarado for smooth and certain singular toric orbifolds upon replacing the…

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

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

We show that the height of a variety over a finitely generated field of characteristic zero can be written as an integral of local heights over the set of places of the field. This allows us to apply our previous work on toric varieties and…

We prove asymptotic formulas for the number of rational points of bounded height on certain blow-ups of the projective space.

We prove an asymptotic formula for the number of integral points of bounded log-anticanonical height on split smooth quintic del Pezzo surfaces over number fields, with respect to one of the lines as the boundary divisor.

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 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.

We establish a formula for the height zeta function for integral points on a class of projective toric varieties. Our method builds on the harmonic analysis approach of Batyrev--Tschinkel for rational points and is applicable even when the…

In the paper we obtain the asymtotic number of integral quadratic polynomials with bounded heights and discriminants as the upper bound of heights tends to infinity.

We establish an asymptotic formula for the number of integral solutions of bounded height for pairs of diagonal quartic equations in $26$ or more variables. In certain cases, pairs in $25$ variables can be handled.

The present note is devoted to an amendment to a recent paper of Ellenberg, Lawrence and Venkatesh. Roughly speaking, the main result here states the subpolynomial growth of the number of integral points with bounded height of a variety…

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.

In this paper we prove a formula for the number of rational points of bounded height relative to all the generators of the cone of effective divisor for a toric variety over a number field.

We formulate a conjecture on the number of integral points of bounded height on log Fano varieties in analogy with Manin's conjecture on the number of rational points of bounded height on Fano varieties. We also give a prediction for the…

We study the distribution of integral points on log varieties.