Related papers: Infinite divisibility of random fields admitting a…
We state some inequalities for m-divisible and infinite divisible characteristic functions. Basing on them we propose a statistical test for a distribution to be infinitely divisible. Keywords: infinite divisible distributions; statistical…
Numerous results on self-reciprocal polynomials over finite fields have been studied. In this paper we generalize some of these to a-self reciprocal polynomials defined in [4]. We consider some properties of the divisibility of a-reciprocal…
We study those integral domains in which every proper ideal can be written as an invertible ideal multiplied by a nonempty product of proper radical ideals.
We determine the finite groups whose real irreducible representations have different degrees.
We prove that the integral powers of the semicircular distribution are freely infinitely divisible. As a byproduct we get another proof of the free infnite divisibility of the classical Gaussian distribution.
We consider various counting questions for irreducible binomials over finite fields. We use various results from analytic number theory to investigate these questions.
We prove that arithmetic is interpretable in any indecomposable polynomial ring (in any set of variables), and in addition we provide an alternative uniform proof of undecidability for all members in this class of rings.
In this paper a free analogous of completely random measure is introduced. Furthermore, a representation theorem is proved for free completely random measures that are free infinitely divisible.
A computable ring is a ring equipped with mechanical procedure to add and multiply elements. In most natural computable integral domains, there is a computational procedure to determine if a given element is prime/irreducible. However,…
In this work infinitely divisible cylindrical probability measures on arbitrary Banach spaces are introduced. The class of infinitely divisible cylindrical probability measures is described in terms of their characteristics, a…
Unrefinable partitions are a subset of partitions into distinct parts which satisfy an additional unrefinability property. More precisely, being an unrefinable partition means that none of the parts can be written as the sum of smaller…
A metric space is indivisible if for any partition of it into finitely many pieces one piece contains an isometric copy of the whole space. Continuing our investigation of indivisible metric spaces, we show that a countable ultrametric…
We classify irreducible unitary representations of the group of all infinite matrices over a $p$-adic field ($p\ne 2$) with integer elements equipped with a natural topology. Any irreducible representation passes through a group $GL$ of…
Let $n$ be a positive integer, and let $R$ be a (possibly infinite dimensional) finitely presented algebra over a computable field of characteristic zero. We describe an algorithm for deciding (in principle) whether $R$ has at most finitely…
We introduce the notion of differential largeness for fields equipped with several commuting derivations (as an analogue to largeness of fields). We lay out the foundations of this new class of "tame" differential fields. We state several…
An algorithm for irreducible decomposition of representations of finite groups over fields of characteristic zero is described. The algorithm uses the fact that the decomposition induces a partition of the invariant inner product into a…
We discuss the phenomenon where an element in a number field is not integrally represented by a given positive definite quadratic form, but becomes integrally represented by this form over a totally real extension of odd degree. We prove…
We classify the automorphic representations (over number fields) and the irreducible admissible representations (over local fields) of unitary groups which are not quasi-split, under the assumption that the same is known for quasi-split…
We study the distribution of principal ideals generated by irreducible elements in an algebraic number field.
It is shown that, given a representation of a quiver over a finite field, one can check in polynomial time whether it is absolutely indecomposable.