Related papers: Another finite field analogue for Appell series F_…
We introduce polynomial sets of $(p,q)$-Appell type and give some of their characterizations. The algebraic properties of the set of all polynomial sequences of $(p,q)$-Appell type are studied. Next, we give a recurrence relation and a…
In this paper, we consider a general form of the analogue of Ramanujan's sum in the ring of polynomials over a finite field. We first prove some multiplicative properties of such functions before considering their finite Fourier series and…
We derive an off-shell recursion relation for correlators that holds at all loop orders. This allows us to prove how generalized amplitudes transform under generic field redefinitions, starting from an assumed behavior of the…
We establish bounds on a finite separable extension of function fields in terms of the relative class number, thus reducing the problem of classifying extensions with a fixed relative class number to a finite computation. We also solve the…
We study Appell functions associated to an arbitrary positive definite lattice $\Lambda$ and a choice of $M\leq {\rm dim}(\Lambda)$ linearly independent vectors $d_r\in \Lambda$, $r=1,\dots,M$. These functions are instances of…
We describe several families of permutation polynomials obtained using functions with linear translators.
This article aims to reinforce the broad applicability of the umbral approach to address complex mathematical challenges and contribute to various scientific and engineering endeavors. The umbral methods are used to reformulate the…
In this paper, by the umbral calculus method, we give a remarkable congruence involving Appell polynomials. Some applications on derangement polynomials are also presented.
The aim of this work is to analyze general infinite sums containing modified Bessel functions of the second kind. In particular we present a method for the construction of a proper asymptotic expansion for such series valid when one of the…
Recursive formulas extending some known $_{2}F_{1}$ and $_{3}F_{2}$ summation formulas by using contiguous relations have been obtained. On the one hand, these recursive equations are quite suitable for symbolic and numerical evaluation by…
In this short note, we introduce an analogue of Wilson's theorem for all nonzero elements $a_1,a_2,...,a_{q-1}$ of a finite filed $\mathbb{F}$ with $|\mathbb{F}|=q\geq 3$, as follows: $$ \sum_{1\leq i_1< i_2<...< i_k\leq…
In this paper, we propose an interpolation formula for periodic functions. This formula can be regarded as an analog of the Sinc approximation, which is an interpolation formula for functions defined on the entire infinite interval.…
The main purpose of this paper is to study generalized (self-) reciprocal Appell polynomials, which play a certain role in connection with Faulhaber-type polynomials. More precisely, we show for any Appell sequence when satisfying a…
We discuss the homological algebra of representation theory of finite dimensional algebras and finite groups. We present various methods for the construction and the study of equivalences of derived categories: local group theory, geometry…
We consider various counting questions for irreducible binomials over finite fields. We use various results from analytic number theory to investigate these questions.
The first part is expository: it explains how finite fields may be used to prove theorems on infinite fields by a reduction mod p process. The second part gives a variant of P.Smith's fixed point theorem which applies in any characteristic.
The aim of the present paper is to introduce Dunkl-Gamma type operators in terms of Appell polynomials and to investigate approximating properties of these operators.
We examine situations, where representations of a finite-dimensional $F$-algebra $A$ defined over a separable extension field $K/F$, have a unique minimal field of definition. Here the base field $F$ is assumed to be a $C_1$-field. In…
For a finite field $\mathbb{F}$, it is a basic result of Galois theory that the fixed field $E$ of $\text{Aut}(\mathbb{F}(x)/\mathbb{F})$ is a proper extension of $\mathbb{F}$. In this expository paper we construct, for all finite fields,…
An exact series expansion for the field radiated by a monopole ring source with angular variation in source strength is derived from a previously developed expression for the field from a finite disk. The derived series can be used…