Related papers: Another finite field analogue for Appell series F_…
The aim of this note is to show the existence of a correspondance between certain algebraic continued fractions in fields of power series over a finite field and automatic sequences in the same finite field. this connection is illustrated…
Using the notion of multivariate lower set interpolation, we construct nodal basis functions for the serendipity family of finite elements, of any order and any dimension. For the purpose of computation, we also show how to express these…
Let $\text{AGL}(1,\Bbb F_q)$ denote the affine linear group of dimension one over the finite field $\Bbb F_q$. We determine the M\"obius function of the lattice of subgroups of $\text{AGL}(1,\Bbb F_q)$.
We show that many infinite classes of permutations over finite fields can be constructed via translators with a large choice of parameters. We first charac- terize some functions having linear translators, based on which several families of…
In this paper, we formulate and prove linear analogues of results concerning matchings in groups. A matching in a group G is a bijection f between two finite subsets A,B of G with the property, motivated by old questions on symmetric…
We prove explicit formulas for certain first and second moment sums of families of Gaussian hypergeometric functions $_{n+1}F_n$, $n\ge1$, over finite fields with $q$ elements where $q$ is an odd prime. This enables us to find an estimate…
Given a finite number of samples of a continuous set-valued function F, mapping an interval to compact subsets of the real line, we develop good approximations of F, which can be computed efficiently.
We provide an elementary derivation of the Bessel analog of the celebrated Riesz composition formula and use the former to effortlessly derive the latter.
Permutation polynomials with explicit constructions over finite fields have long been a topic of great interest in number theory. In recent years, by applying linear translators of functions from $\mathbb{F}_{q^n}$ to $\mathbb{F}_q$, many…
Several infinite products are studied that satisfy the transformation relation of the type $f(\alpha)=f(1/\alpha)$. For certain values of the parameters these infinite products reduce to modular forms. Finite counterparts of these infinite…
In this paper we present an equivalent statement to the Jacobian conjecture. For a polynomial map F on an affine space of dimension n, we define recursively n finite sequences of polynomials. We give an equivalent condition to the…
We describe a new source of counterexamples to the so-called integral Hodge and integral Tate conjectures. As in the other known counterexamples to the integral Tate conjecture over finite fields, ours are approximations of the classifying…
In this article, we give a sequence of operators for producing an approximation result. The relation between the rate of approximation of sequence operators including Dunkl variant of exponential function with first and second-order modulus…
We present the proof of the equivalence theorem in quantum field theory which is based on a formulation of this problem in the field-antifield formalism. As an example, we consider a model in which a different choices of natural finite…
We establish a q-analogue of Wolstenholme's harmonic series congruence.
This paper extends Hopf-Galois theory to infinite field extensions and provides a natural definition of subextensions. For separable (possibly infinite) Hopf-Galois extensions, it provides a Galois correspondence. This correspondence also…
Tnis paper deals with some special integral transforms in the setting of quaternionic valued slice polyanalytic functions. In particular, using the polyanalytic Fueter mappings it is possible to construct a new family of polynomials which…
It is well known that there exists a significant equivalence between the vector space $\mathbb{F}_{q}^n$ and the finite fields $\mathbb{F}_{q^n}$, and many scholars often view them as the same in most contexts. However, the precise…
We state and prove a function field analogue of Furusho for multiple zeta values.
In this paper, we will introduce Bell numbers $D(n)$ of type $D$ as an analogue to the classical Bell numbers related to all the partitions of the set $[n]$. Then based on a signed set partition of type $D$, we will construct the recurrence…