Related papers: Word Values in p-Adic and Adelic Groups
In this paper we construct examples of p-groups with derived length three and three character degrees.
We give an explicit classification of translation-invariant, Lorentz-invariant continuous valuations on convex sets. We also classify the Lorentz-invariant even generalized valuations.
In this note, we study the finite groups whose Chermak-Delgado measure has exactly two values. They determine an interesting class of $p$-groups containing cyclic groups of prime order and extraspecial $p$-groups.
In this paper we improve our previous results on classification of groups of points on abelian varieties over finite fields. The classification is given in terms of the Weil polynomial of abelian varieties in a given $k$-isogeny class.
In this paper, we introduce personalized word embeddings, and examine their value for language modeling. We compare the performance of our proposed prediction model when using personalized versus generic word representations, and study how…
We classify crossed product gradings for arbitrary groups and fields up to several equivalence relations in terms of group actions and their orbits.
We obtain asymptotic and exact formulae of growth functions for some families of $n$-valued coset groups. We also describe connections between the theory of $n$-valued groups and Symbolic Dynamics.
Given a group word $w$ and a group $G$, the set of $w$-values in $G$ is denoted by $G_w$ and the verbal subgroup $w(G)$ is the one generated by $G_w$. In the present paper we consider profinite groups admitting a word $w$ such that the…
We give a brief survey of recent results on word maps on simple groups and polynomial maps on simple associative and Lie algebras. Our focus is on parallelism between these theories, allowing one to state many new open problems and giving…
We use the theory of motivic integration in order to give a geometric explanation of the behavior of some p-adic integrals.
In this short survey we look at a few basic features of p-adic numbers, somewhat with the point of view of a classical analyst. In particular, with p-adic numbers one has arithmetic operations and a norm, just as for real or complex…
We develop a theory of k-partitions of the set of infinite words recognizable by classes of finite automata. The theory enables to complete proofs of existing results about topological classifications of the (aperiodic) omega-regular…
We develop JSJ decomposition theory of pro-p groups.
In the introduction of this paper we discuss a possible approach to the unitarizability problem for classical p-adic groups. In this paper we give some very limited support that such approach is not without chance. In a forthcoming paper we…
The purpose of this paper is to give the explicit formulae of p-adic l-functions and sums of powers which are related to Euler numbers.
This document contains the notes of a lecture I gave at the "Journ\'ees Nationales du Calcul Formel" (JNCF) on January 2017. The aim of the lecture was to discuss low-level algorithmics for p-adic numbers. It is divided into two main parts:…
After a brief review of the idea and main results of the original p-adic string work, I describe the recent interest in p-adic strings in the context of AdS/CFT duality
The authors study the central values of L-functions in certain families; in particular they bound the sum of the cubes of these values.Contents:
We study algebraic, combinatorial and topological properties of the set of preorders on a group, and the set of valuations on a field. We show strong analogies between these two kinds of sets and develop a dictionary for these ones. Among…
We investigate two notions about descriptions of groups using first-order language: quasi-finite axiomatizability, concerning infinite groups, and polylogarithmic compressibility, concerning classes of finite groups.