Related papers: Property tau in positive characteristic

An important result of Bilu deals with the equidistribution of the Galois orbits of a sequence $(\alpha_n)_n$ in $\overline{\mathbb{Q}}^*$. Here, we prove a quantitative equidistribution theorem for a sequence of finite subsets in…

We develop a computational framework for the statistical characterization of Galois characters with finite image, with application to characterizing Galois groups and establishing equivalence of characters of finite images of…

It is well known Heyde's characterization of the Gaussian distribution on the real line: Let $\xi_1, \xi_2,\dots, \xi_n$, $n\ge 2,$ be independent random variables, let $\alpha_j, \beta_j$ be nonzero constants such that…

In this paper, we prove the equidistribution property of high-frequency eigensections of a certain series of unitary flat bundles, using the mixture of semiclassical and geometric quantizations.

We show that a suitable quantitative Fatou Theorem characterizes uniform rectifiability in the codimension 1 case.

We prove the Manin--Peyre equidistribution principle for smooth projective split toric varieties over the rational numbers. That is, rational points of bounded anticanonical height outside of the boundary divisors are equidistributed with…

Goulden-Rattan polynomials give the exact value of the subdominant part of the normalized characters of the symmetric groups in terms of certain quantities ($C_i$) which describe the macroscopic shape of the Young diagram. The…

We prove a positive characteristic version of Ax's theorem on the intersection of an algebraic subvariety and an analytic subgroup of an algebraic group. Our result is stated in a more general context of a formal map between an algebraic…

We obtain a characterization of property (T) for von Neumann algebras in terms of 1-cohomology similar to the Delorme-Guichardet Theorem for groups.

We discuss special properties of the spaces of characters and positive definite functions, as well as their associated dynamics, for arithmetic groups of product type. Axiomatizing these properties, we define the notions of charmenability…

We prove an Erd\H{o}s--Tur\'an type inequality for compact Lie groups, from which we deduce an effective version of Deligne's equidistribution theorem.

In this paper we show that quotients of smooth projective toric varieties by $\mu_p$ in positive characteristics $p$ are toric varieties.

We introduce a notion of topological property (T) for \'etale groupoids. This simultaneously generalizes Kazhdan's property (T) for groups and geometric property (T) for coarse spaces. One main goal is to use this property (T) to prove the…

We show that, under fairly general conditions, many elements of a p-adic group can be well approximated by a product whose factors have properties that are helpful in performing explicit character computations.

In this article, we prove the boundedness of minimal slopes of adelic line bundles over function fields of characteristic 0. This can be applied to prove the equidistribution of generic and small points with respect to a big and…

We prove an effective equidistribution theorem for semisimple closed orbits on compact adelic quotients. The obtained error depends polynomially on the minimal complexity of intermediate orbits and the complexity of the ambient space. The…

Albiac and Wojtaszczyk introduced property (A) to characterize $1$-greedy bases. Later, Dilworth et al. generalized the concept to $C$-property (A), where the case $C = 1$ gives property (A). They (among other results) characterized greedy…

We prove a new quantum variance estimate for toral eigenfunctions. As an application, we show that, given any orthonormal basis of toral eigenfunctions and any smooth embedded hypersurface with nonvanishing principal curvatures, there…

Using functional and harmonic analysis methods, we study Kazhdan sets in topological groups which do not necessarily have Property (T). We provide a new criterion for a generating subset $Q$ of a group $G$ to be a Kazhdan set; it relies on…

We show how the problem of estimating conditional Kendall's tau can be rewritten as a classification task. Conditional Kendall's tau is a conditional dependence parameter that is a characteristic of a given pair of random variables. The…