Related papers: Hensel minimality, $p$-adic exponentiation and Tat…

Let $K$ be a local field of residue characteristic $p$. Let $C$ be a curve over $K$ whose minimal proper regular model has totally degenerate semi-stable reduction. Under certain hypotheses, we compute the prime-to-$p$ rational torsion…

In this paper we investigate $p$-adic self-similar sets and $p$-adic self-similar measures. We show that $p$-adic self-similar sets are $p$-adic path set fractals, and that the converse is not necessarily true. For $p$-adic self-similar…

This paper introduces and studies a class of Weyl-type algebras \(A_{p,t,\cA} = \Weyl{e^{\pm x^{p} e^{t x}},\; e^{\cA x},\; x^{\cA}}\) constructed over exponential-polynomial rings, where \(\FF\) is a field of characteristic zero, \(\cA\)…

The steady-state currents and densities of a one-dimensional totally asymmetric exclusion process (TASEP) with particles that occlude an integer number ($d$) of lattice sites are computed using various mean field approximations and Monte…

Recently, a new concept called the $c$-differential uniformity was proposed by Ellingsen et al. (2020), which allows to simplify some types of differential cryptanalysis. Since then, finding functions having low $c$-differential uniformity…

The P\'al inequality is a classical result which asserts that among all planar convex sets of given width the equilateral triangle is the one of minimal area. In this paper we prove three quantitative versions of this inequality, by…

Permutation polynomials over finite fields are fundamental objects as they are used in various theoretical and practical applications in cryptography, coding theory, combinatorial design, and related topics. This family of polynomials…

This article is an exposition of recent results on self-similar sets, asserting that if the dimension is smaller than the trivial upper bound then there are almost overlaps between cylinders. We give a heuristic derivation of the theorem…

A discrete-time totally asymmetric simple exclusion process on a lattice with open boundaries is considered. There are particles of different types. The type of a particle is characterized by the probability that a particle moves to a…

We establish a transfer of unitarity for a Bernstein component of the category of smooth representations of a reductive p-adic group to the associated Hecke algebra, in the framework of the theory of types, whenever the Hecke algebra is an…

The author's work with Murnaghan on distinguished tame supercuspidal representations is re-examined using a simplified treatment of Jiu-Kang Yu's construction of tame supercuspidal representations of $p$-adic reductive groups. This leads to…

We show, using the techniques developed in arXiv:2504.06444 and arXiv:2305.11139, that dagger algebras and Tate algebras in the sense of Berkovich in prime characteristic $p > 0$ have intersection flat Frobenius. Equivalently, if $S$ is…

In this paper we introduce techniques from complex harmonic analysis to prove a weaker version of the Geometric Arveson-Douglas Conjecture for complex analytic subsets that is smooth on the boundary of the unit ball and intersects…

We study the problem of computing minimal distinguishing formulas for non-bisimilar states in finite LTSs. We show that this is NP-hard if the size of the formula must be minimal. Similarly, the existence of a short distinguishing trace is…

Let $n\geq 0$ and $r>0$ be integers. Let $\mathcal{O}_{X, x}^{h}$ be the henselization of the local ring $\mathcal{O}_{X, x}$ of a scheme $X$ at a point $x\in X$. For a normal crossing variety $Y$ over the spectrum of a field $k$ of…

We study the question of testing structured properties (classes) of discrete distributions. Specifically, given sample access to an arbitrary distribution $D$ over $[n]$ and a property $\mathcal{P}$, the goal is to distinguish between…

This paper exploits adjacencies between the orbits of an ordered set P and a consequence of the classification of finite simple groups to, in many cases, exponentially bound the number of automorphisms. Results clearly identify the…

Let (A,\lambda) be a principally polarized abelian variety defined over a global field k, and let \Sha(A) be its Shafarevich-Tate group. Let \Sha(A)_\nd denote the quotient of \Sha(A) by its maximal divisible subgroup. Cassels and Tate…

We develop a theory of minors for alternating dimaps --- orientably embedded digraphs where, at each vertex, the incident edges (taken in the order given by the embedding) are directed alternately into, and out of, the vertex. We show that…

We further develop the abstract representation theory of affine Hecke algebras with arbitrary positive parameters. We establish analogues of several results that are known for reductive p-adic groups. These include: the relation between…