Related papers: An Appell series over finite fields
Let G be the space of generating functions of a periodic infinite order linear recurrence. In this paper we provide an explicit procedure for computing a basis of G.
Permutation polynomials are an interesting subject of mathematics and have applications in other areas of mathematics and engineering. In this paper, we develop general theorems on permutation polynomials over finite fields. As a…
We continue our study on counting irreducible polynomials over a finite field with prescribed coefficients. We set up a general combinatorial framework using generating functions with coefficients from a group algebra which is generated by…
Motivated by the effective impact of the Pascal functional and the Wronskian matrices, we investigate several identities and differential equation for the Sheffer-Appell polynomial sequence by using matrix algebra. The matrix approach,…
A new $q$-analogue of Appell polynomial sequences and their generalizations are introduced and their main characterizations are proved. As consequences new $q$-analogue of Bernoulli and Euler polynomials and numbers is introduced, their…
We suggest an approximation for the zero-balanced Appell hypergeometric function $F_1$ near the singular point $(1,1)$. Our approximation can be viewed as a generalization of Ramanujan's approximation for zero-balanced ${_2F_1}$ and is…
We propose several techniques to construct complete permutation polynomials of finite fields by virtue of complete permutations of subfields. In some special cases, any complete permutation polynomials over a finite field can be used to…
We describe several families of permutation polynomials obtained using functions with linear translators.
In this expository article we collect the integer sequences that count several different types of matrices over finite fields and provide references to the Online Encyclopedia of Integer Sequences (OEIS). Section 1 contains the sequences,…
We define a finite-field version of Appell-Lauricella hypergeometric functions built from period functions in several variables, paralleling the development by Fuselier, et. al in the single variable case. We develop geometric connections…
We define a hypergeometric function over finite fields which is an analogue of the classical generalized hypergeometric series. We prove that this function satisfies many transformation and summation formulas. Some of these results are…
Kamp\'e de F\'eriet hypergeometric functions are two-variable hypergeometric functions, which are a generalization of Appell's functions. It is known that they satisfy many reduction and summation formulas. In this paper, we define Kamp\'e…
We introduce a number field analogue of the Mertens conjecture and demonstrate its falsity for all but finitely many number fields of any given degree. We establish the existence of a logarithmic limiting distribution for the analogous…
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 study the structure of an algebraically closed field with extra function resembling the classical exponentiation on complex numbers.
We construct the Langlands correspondence for connected reductive groups over finite fields, which we call the finite Langlands correspondence. We discuss also its relation with the categorical local Langlands correspondence.
We present new classes of permutation polynomials over finite fields.
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…
In this paper, by the umbral calculus method, we give a remarkable congruence involving Appell polynomials. Some applications on derangement polynomials are also presented.
We present new analytic continuation formulas for the Appell $F_4(a,b;c,d;x,y)$ double hypergeometric series where $d=a-b+1$, which allows quadratic transformations of the Gauss ${}_2F_1$ hypergeometric function to be used in the…