Related papers: A congruence property of irreducible Laguerre poly…

Following our earlier work, where doubly indexed and irreducible over Q two-variable Laguerre polynomials were introduced, we prove for such polynomials some recurrence formulas and obtain a generating function. In addition, we show how…

We describe a congruence property of solvable polynomials over Q, based on the irreducibility of cyclotomic polynomials over number fields that meet certain conditions.

In this paper, we describe a congruence property of solvable polynomials with coefficients in the Gaussian field Q(i).

We prove that the Eulerian polynomial satisfies certain polynomial congruences. Furthermore, these congruences characterize the Eulerian polynomial.

We obtain explicit upper bounds for the number of irreducible factors for a class of compositions of polynomials in several variables over a given field. In particular, some irreducibility criteria are given for this class of compositions…

In this article, we derive a congruence property of particular sum rules involving prime numbers. The resulting expression involves Bernoulli numbers and polynomials, for which we obtain, as a consequence, a general congruence relation as…

We present a theorem about irreducibility of a polynomial that is the resultant of two others polynomials. The proof of this fact is based on the field theory. We also consider the converse theorem and some examples.

We show that the coefficients of the three-term recurrence relation for orthogonal polynomials with respect to a semi-classical extension of the Laguerre weight satisfy the fourth Painlev\'e equation when viewed as functions of one of the…

We review properties of confluent functions and the closely related Laguerre polynomials, and determine their bilinear integrals. As is well-known, these integrals are convergent only for a limited range of parameters. However, when one…

In the paper, we generalize some congruences of Lehmer for general composite numbers.

We compute the compactly supported Euler characteristic of the space of degree $d$ irreducible polynomials in $n$ variables with real coefficients and show that the values are given by the digits in the so-called balanced binary expansion…

In this paper, by the umbral calculus method, we give a remarkable congruence involving Appell polynomials. Some applications on derangement polynomials are also presented.

In a previous paper we deformed Hermite polynomials to three associated polynomials .Here we apply the same deformation to Laguerre polynomials .

In this article, we give two different sufficient conditions for the irreducibility of a polynomial of more than one variable, over the field of complex numbers, that can be written as a sum of two polynomials which depend on mutually…

In this paper, we propose a generalization of a congruence due to Carlitz.

A Lagrange Theorem in dimension 2 is proved, for a particular two-dimensional algorithm, with a very natural geometrical definition. Dirichlet-type properties for the convergence of the algorithm are also proved. These properties procced…

We give a formula and an estimation for the number of irreducible polynomials in two (or more) variables over a finite field.

The explicit double sum for the associated Laguerre polynomials is derived combinatorially. The moments are described using certain statistics on permutations and permutation tableaux. Another derivation of the double sum is provided using…

In this paper, we state and prove some congruence properties for the trinomial coeficients, one of which is similar to the Wolstenholme's theorem.

For the oscillator-like systems, connected with the Laguerre, Legendre and Chebyshev polynomials coherent states of Glauber-Barut-Girardello type are defined. The suggested construction can be applied to each system of orthogonal…