Related papers: Points of bounded height on weighted projective sp…

We give a sharp upper bound on the multiplicity of a fake weighted projective space with at worst canonical singularities. This is equivalent to giving a sharp upper bound on the index of the sublattice generated by the vertices of a…

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 present bounds for the degree and the height of the polynomials arising in some central problems in effective algebraic geometry including the implicitation of rational maps and the effective Nullstellensatz over a variety. Our treatment…

The purpose of this paper is to give a linear and effective height inequality for algebraic points on curves over functional fields. Our height inequality can be viewed as the logarithmic canonical class inequality of a punctured curve over…

We give upper and lower bounds for the number of rational points on Prym varieties over finite fields. Moreover, we determine the exact maximum and minimum number of rational points on Prym varieties of dimension 2.

In this paper, we prove the boundedness of the Bergman projection on weighted mixed norm spaces of the upper-half space for some weights that are constructed using the logarithm function and growth functions. Our necessary and sufficient…

We determine upper bounds on the number of rational points of an affine or projective algebraic set defined over an extension of a finite field by a system of polynomial equations, including the case where the algebraic set is not defined…

Using the circle method, we count integer points on complete intersections in biprojective space in boxes of different side length, provided the number of variables is large enough depending on the degree of the defining equations and…

We give effective bounds for the class number of any algebraic function field of genus $g$ defined over a finite field. These bounds depend on the possibly partial information on the number of places on each degree $\leq g$. Such bounds are…

An upper bound of the expected order of magnitude is established for the number of rational points of bounded height on Ch\^atelet surfaces defined over the rationals.

In this paper, we study several definitions of generalized rank weights for arbitrary finite extensions of fields. We prove that all these definitions coincide, generalizing known results for extensions of finite fields.

We establish asymptotic formulas for counting rational points near finite type curves on the plane, generalizing Huang's result.

We study the set of algebraic numbers of bounded height and bounded degree where an analytic transcendental function takes algebraic values.

Let $\F_p = \Z/p\Z$. The \emph{height} of a point $\mathbf{a}=(a_1,..., a_d) \in \F_p^d$ is $h_p(\mathbf{a}) = \min \left\{\sum_{i=1}^d (ka_i \mod p) : k=1,...,p-1\right\}.$ Explicit formulas and estimates are obtained for the values of the…

We improve a bound due to the second author on number of rational points on smooth surfaces in $\mathbb{P}^3$ over finite fields and look at families of surfaces that achieve or nearly achieve this bound, for which we compute their exact…

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 $\mathbb{Q}$.

In this article we studied the relationship between metric spaces and multiplicative metric spaces. Also, we pointed out some fixed and common fixed point results under some contractive conditions in multiplicative metric spaces can be…

We give a construction of singular curves with many rational points over finite fields. This construction enables us to prove some results on the maximum number of rational points on an absolutely irreducible projective algebraic curve…

In this paper, we give some counting results on integer polynomials of fixed degree and bounded height whose distinct non-zero roots are multiplicatively dependent. These include sharp lower bounds, upper bounds and asymptotic formulas for…

We use the circle method to count $\mathbb{F}_q(t)$-rational points of bounded naive height on a quadric hypersurface $X\subseteq \mathbb{P}^{n-1}$ defined over $\mathbb{F}_q$, provided that $\mathrm{char}(\mathbb{F}_q)>2$ and $n\ge 3$.…