Related papers: Good height functions on quasi-projective varietie…

We prove the existence of a gap around zero for canonical height functions associated to endomorphisms of projective spaces defined over complex function fields. We also prove that if the rational points of height zero are Zariski dense,…

Let $ S $ be a quasi-projective smooth variety over complex field $ \mathbb{C} $. For a smooth projective morphism $ \pi:X\to S $, we will introduce a new height pairing \begin{align*} CH^p_{\hom}(X/S) \times CH^q_{\hom}(X/S) \to…

We propose a framework to give a precise meaning to the intuitive notion of "family of real forms of a variety parametrised by a variety" and study some fundamental properties of this notion. As an illustration, for any $n \geq 1$, we…

Although models for count data with over-dispersion have been widely considered in the literature, models for under-dispersion -- the opposite phenomenon -- have received less attention as it is only relatively common in particular research…

Ultrafunctions are a particular class of functions defined on a Non Archimedean field E. They have been introduced and studied in some previous works. In this paper we develop the notion of fine ultrafunctions which improves the older…

We construct a class of real-valued nonnegative binary functions on a set of jointly distributed random variables, which satisfy the triangle inequality and vanish at identical arguments (pseudo-quasi-metrics). These functions are useful in…

We introduce a ``geometric'' method to bound periods of automorphic forms. The key features of this method are the use of equidistribution results in place of mean value theorems, and the systematic use of mixing and the spectral gap.…

In this paper, we propose a new framework for studying the distribution of rational points on DM stacks of positive characteristic. Our primary focus is on wild stacks, which existing frameworks do not address. There was not even a…

We bound the length of the periodic part of the orbit of a preperiodic rational subvariety via good reduction information. This bound depends only on the degree of the map, the degree of the subvariety, the dimension of the projective…

We prove asymptotic formulas for the number of rational points of bounded height on smooth equivariant compactifications of the affine space. (Nous \'etablissons un d\'eveloppement asymptotique du nombre de points rationnels de hauteur…

Functionals in geometric probability are often expressed as sums of bounded functions exhibiting exponential stabilization. Methods based on cumulant techniques and exponential modifications of measures show that such functionals satisfy…

We present projective descriptions of classical spaces of functions and distributions. More precisely, we provide descriptions of these spaces by semi-norms which are defined by a combination of classical norms and multiplication or…

Here we describe the distribution of rational points on the Hilbert scheme of two points in the projective plane. More specifically, we explicitly describe a two-parameter family of height functions $H_{s, t}$, such that the height function…

Probabilistic submeasures generalizing the classical (numerical) submeasures are introduced and discussed in connection with some classes of aggregation functions. A special attention is paid to triangular norm-based probabilistic…

The power structure over the Grothendieck (semi)ring of complex quasi-projective varieties constructed by the authors is used to express the generating series of classes of Hilbert schemes of zero-dimensional subschemes on a smooth…

The densities of small linear structures (such as arithmetic progressions) in subsets of Abelian groups can be expressed as certain analytic averages involving linear forms. Higher-order Fourier analysis examines such averages by…

We provide complete structural theorems for the so-called quasiasymptotic behavior of non-quasianalytic ultradistributions. As an application of these results, we obtain descriptions of quasiasymptotic properties of regularizations at the…

In this paper subdivision schemes, which are used for functions approximation and curves generation, are considered. In classical case, for the functions defined on the real line, the theory of subdivision schemes is widely known due to…

Using techniques of the theory of semigroups of linear operators we study the question of approximating solutions to equations governing diffusion in thin layers separated by a semi-permeable membrane. We show that as thickness of the…

Several recent papers construct auxiliary polynomials to bound the Weil height of certain classes of algebraic numbers from below. Following these techniques, the author gave a general method for introducing auxiliary polynomials to…