Related papers: Equidistribution over function fields

The aim of this paper is to prove a theorem of Ax-Lindemann type for complex semi-abelian varieties as an application of a big Picard theorem proved by the author in 1981, and then apply it to prove a theorem of classical Manin-Mumford…

Generalized polynomials are mappings obtained from the conventional polynomials by the use of operations of addition, multiplication and taking the integer part. Extending the classical theorem of H. Weyl on equidistribution of polynomials,…

We prove that the torsion points of an abelian variety are equidistributed over the corresponding berkovich space with respect to the canonical measure.

An action of a complex reductive group $\mathrm G$ on a smooth projective variety $X$ is regular when all regular unipotent elements in $\mathrm G$ act with finitely many fixed points. Then the complex $\mathrm G$-equivariant cohomology…

For a reductive group scheme over a regular semi-local ring, we prove an equivarinat version of the Gersten conjecture. We draw some interesting consequences for the representation rings of such reductive group schemes. We also prove the…

Let $(X,\mathfrak{B},\mu)$ be a Borel probability space. Let $T_n: X\rightarrow X$ be a sequence of continuous transformations on $X$. Let $\nu$ be a probability measure on $X$ such that $\frac{1}{N}\sum_{n=1}^N (T_n)_\ast \nu \rightarrow…

We deduce an effective version of Schmidt's subspace theorem on a smooth projective variety X over function fields of characteristic zero for hypersurfaces located in N-subgeneral position with respect to X.

We use tools of additive combinatorics for the study of subvarieties defined by {\it high rank} families of polynomials in high dimensional $\mathbb{F} _q$-vector spaces. In the first, analytic part of the paper we prove a number properties…

We describe a generalization of the voter model on complex networks that encompasses different sources of degree-related heterogeneity and that is amenable to direct analytical solution by applying the standard methods of heterogeneous…

We prove equidistribution of Weierstrass points on Berkovich curves. Let $X$ be a smooth proper curve of positive genus over a complete algebraically closed non-Archimedean field $K$ of equal characteristic zero with a non-trivial…

We prove equidistribution theorems for a family of holomorphic Siegel cusp forms of general degree in the level aspect. Our main contribution is to estimate unipotent contributions for general degree in the geometric side of Arthur's…

In this paper, we give an equivalent condition for an abelian variety over a finite field to have multiplication by a quaternion algebra over a number field. We prove the result by combining Tate's classification of the endomorphism…

In this paper an iterated function system on the space of distribution functions is built. The inverse problem is introduced and studied by convex optimization problems. Some applications of this method to approximation of distribution…

In this paper, we prove several Ax-Schanuel type results for uniformizers of geometric structures; our general results describe the differential algebraic relations between the solutions of the partial differential equations satisfied by…

Let $X$ be an algebraic variety over a finite field $\bF_q$, homogeneous under a linear algebraic group. We show that the number of rational points of $X$ over $\bF_{q^n}$ is a periodic polynomial function of $q^n$ with integer…

We prove some distribution results for the $k$-fold divisor function in arithmetic progressions to moduli that exceed the square-root of length $X$ of the sum, with appropriate constrains and averaging on the moduli, saving a power of $X$…

For a wide class of sequences of integer domains $\mathcal{D}_n\subset\mathbb{N}^d$, $n\in\mathbb{N}$, we prove distributional limit theorems for $F(X_1^{(n)},\ldots,X_d^{(n)})$, where $F$ is a multivariate multiplicative function and…

In this paper we generalize a result of Montgomery and Vaughan regarding exponential sums with multiplicative coefcients to the setting of Weyl sums. As applications, we establish a joint equidistribution result for roots of polynomial…

We study equidistribution of certain subsets of periodic orbits for subshifts of finite type. Our results solely rely on the growth of these subsets. As a consequence, effective equidistribution results are obtained for both hyperbolic…

We define partially ample subvarieties of projective varieties, generalizing Ottem's work on ample subvarieties, and show their ubiquity. As an application, we obtain a connectedness result for pre-images of subvarieties by morphisms,…