Related papers: Abelian $p$-extensions and additive polynomials
We present a few factorizations of polynomials over finite fields. These factorizations are related to traces, compositions of polynomials and binomial coefficients. As a corollary we obtain a description of all irreducible polynomials…
We give an explicit description of the category of central extensions of a group scheme by a sheaf of Abelian groups. Based on this, we describe a framework for computing with central extensions of finite commutative group schemes, torsors…
In this paper, we classify the possible group structures on the set of $R$-valued points of an abelian variety, where $R$ is any real closed field. We make use of a family of abelian varieties that, in effect, allows one to quantify over…
We propose a conjectural characterization of when the dynamical Galois group associated to a polynomial is abelian, and we prove our conjecture in several cases, including the stable quadratic case over ${\mathbb Q}$. In the postcritically…
We introduce a generalization of the Dobinski relation through which we define a family of Bell-type numbers and polynomials. For all these sequences we find the weight function of the moment problem and give their generating functions. We…
We construct infinite families of irreducible supersingular mod $p$ representations of $\mathrm{GL}_2(F)$ with $\mathrm{GL}_2(\mathcal{O}_F)$-socle compatible with Serre's modularity conjecture, where $F / \mathbb{Q}_p$ is any finite…
We consider elliptic partial differential equations with diffusion coefficients that depend affinely on countably many parameters. We study the summability properties of polynomial expansions of the function mapping parameter values to…
A generalization of the generating function for Gegenbauer polynomials is introduced whose coefficients are given in terms of associated Legendre functions of the second kind. We discuss how our expansion represents a generalization of…
In the paper, a method of describing the outer derivations of the group algebra of a finitely presentable group is given. The description of derivations is given in terms of characters of the groupoid of the adjoint action of the group.
For a two parameter family of Bernoulli numbers $B_{n, p}$ the exponential generating function is derived by elementary methods.
We extend a conjecture of Kimberley-Robertson on the abelianizations of certain square complex groups.
We show the existence of and explicitly construct generic polynomials for various groups, over fields of positive characteristic. The methods we develop apply to a broad class of connected linear algebraic groups defined over finite fields…
We construct a canonical family of elements in the reduced exterior power lattices of the unit groups of global fields. We prove that this family recovers the theory of cyclotomic elements in real abelian fields and also establish detailed…
In this paper, we present a probabilistic extension of the Fubini polynomials and numbers associated with a random variable satisfying some appropriate moment conditions. We obtain the exponential generating function and an integral…
In this paper we generalize and specialize generating functions for classical orthogonal polynomials, namely Jacobi, Gegenbauer, Chebyshev and Legendre polynomials. We derive a generalization of the generating function for Gegenbauer…
We establish an alternative, ``perpendicular" collection of generating functions for the coefficients of Gaussian polynomials, $\begin{bmatrix}N+m\\m\end{bmatrix}_q$. We provide a general characterization of these perpendicular generating…
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…
This note provides an insight to the diophantine properties of abelian surfaces with quaternionic multiplication over number fields. We study the fields of definition of the endomorphisms on these abelian varieties and the images of the…
New methods for derivation of Bell polynomials of the second kind are presented. The methods are based on an ordinary generating function and its composita. The relation between a composita and a Bell polynomial is demonstrated. Main…
The aim of this paper is to further study some properties and identities on the degenerate Fubini and the degenerate Bell polynomials which are degenerate versions of the Fubini and the Bell polynomials, respectively. Especially, we find…