Related papers: On multiplicatively dependent vectors of algebraic…

In this paper, we study the distribution of multiplicatively dependent vectors. For example, although they have zero Lebesgue measure, they are everywhere dense both in $\mathbb{R}^n$ and $\mathbb{C}^n$. We also study this property in a…

We establish asymptotic formulae for the number of biquadratic number fields of bounded discriminant that can be embedded into a quaternionic or a dihedral extension. To prove these results, we express the solvability of these inverse…

Let $E_1, \ldots, E_s $ be $s$, not necessary distinct, elliptic curves over $\mathbb{Q}$. We give upper bounds on the frequency of $s$-tuples of points in $E_1(\mathbb{Q})\times \ldots \times E_s(\mathbb{Q})$ whose denominators or…

Using recent results from the theory of integer points close to smooth curves, we give an asymptotic formula for the distribution of values of a class of integer-valued prime-independent multiplicative functions.

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.

We generalize the absolute logarithmic Weil height from elements of the multiplicative group of algebraic numbers modulo torsion, to finitely generated subgoups. The height of a finitely generated subgroup is shown to equal the volume of a…

We discuss heuristic asymptotic formulae for the number of pairing-friendly abelian varieties over prime fields, generalizing previous work of one of the authors arXiv:math1107.0307

We give lower bounds on the number of effective divisors of degree $\leq g-1$ with respect to the number of places of certain degrees of an algebraic function field of genus $g$ defined over a finite field. We deduce lower bounds and…

In this paper we introduce the concept of Abelian integrals in differential equations for an arbitrary vector bundle on $\P1$ with a meromorphic connection. In this general context we give an upper bound for the numbers we are looking for.

In this note we give exact formulas (and asymptotics) for the number of rational points of bounded height on weighted projective stacks over global function fields.

In this paper we study a sequence involving the prime numbers by deriving two asymptotic formulas and finding new upper and lower bounds, which improve the currently known estimates.

This article deals with the multiple values and algebraic dependences problem of meromorphic mappings sharing moving hyperplanes in projective space. We give some algebraic dependences theorems for meromorphic mappings sharing moving…

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

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

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

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 consider the set $\mathcal{M}_n(\mathbb Z; H)$ of $n\times n$-matrices with integer elements of size at most $H$ and obtain a new upper bound on the number of matrices from $\mathcal{M}_n(\mathbb Z; H)$ with a given characteristic…

We count the number of irreducible polynomials in several variables of a given degree over a finite field. The results are expressed in terms of a generating series, an exact formula and an asymptotic approximation. We also consider the…

Several notions of multiplicativity are introduced for forms of degree $d\geq 3$ over a field of characteristic 0 or greater than d. Examples of multiplicative and strongly multiplicative forms of higher degree are given. Conditions…

Asymptotics are given for the number of rational points in the domain of a morphism of weighted projective stacks whose images have bounded height and satisfy a (possibly infinite) set of local conditions. As a consequence we obtain results…