Related papers: A note about zonal polynomials

We provide upper bounds for the cardinality of the value set of a polynomial map in several variables over a finite field. These bounds generalize earlier bounds for univariate polynomials.

We introduce two notions of quandle polynomials for G-families of quandles: the quandle polynomial of the associated quandle and a G-family polynomial with coefficients in the group ring of G. As an application we define image subquandle…

In this paper, we generalize Gauss' lemma for polynomials over subtractive factorial semidomains.

Generating functions and functional equations of Dickson polynomials of the first and second kind are derived and continued analytically. These formulae are expressed in terms of the incomplete gamma function over complex variables of the…

Limiting cases are studied of the Koornwinder-Macdonald multivariable generalization of the Askey-Wilson polynomials. We recover recently and not so recently introduced families of hypergeometric orthogonal polynomials in several variables…

The objective of this paper is to derive symmetric property of (h,q)-Zeta function with weight alpha. By using this property, we give some interesting identities for (h,q)-Genocchi polynomials with weight alpha. As a result, our…

By polynomial (or extended binomial) coefficients, we mean the coefficients in the expansion of integral powers, positive and negative, of the polynomial $1+t +\cdots +t^{m}$; $m\geq 1$ being a fixed integer. We will establish several…

We investigate factorizability of a quadratic split quaternion polynomial. In addition to inequality conditions for existence of such factorization, we provide lucid geometric interpretations in the projective space over the split…

Multivariable generalizations of the continuous Hahn and Wilson polynomials are introduced as eigenfunctions of rational Ruijsenaars type difference systems with an external field.

We give a first-order definition of key polynomials, we show the links with previous definitions, that it is relevant to study key degrees, and to use a kind of valuations that we call partially multiplicative. We also prove or reprove…

In this paper, we present some double inequalities involving certain ratios of the Gamma function. These results are further generalizations of several previous results. The approach is based on the monotonicity properties of some functions…

We survey various classical results on invariants of polynomials, or equivalently, of binary forms, focussing on explicit calculations for invariants of polynomials of degrees 2, 3, 4.

For bounded domains, eigenvalues and eigenfunctions of double layer potentials are considered. The aim of this paper is to establish some relationships between eigenvalues, eigenfunctions and the geometry of domain boundaries.

We present a general survey of some recent developments regarding the construction of compact quantum symmetric spaces and the analysis of their zonal spherical functions in terms of $q$-orthogonal polynomials. In particular, we define a…

In this paper we study (h,q)-zeta functions associated with (h,q)-Bernoulli numbers and polynomials.

We complete the study of some periods of polynomials in (n+1) variables with (n+2) monomials in computing the behavior of these periods in the natural parameter for such a polynomial.

The special values of multiple polylogarithms, which including multiple zeta values, appear some fields of mathematics and physics. Many kinds of their linear relations are investigated as well as their algebraic relations. From the…

We show that (as conjectured by Lin and Wang) when a Vassiliev invariant of type $m$ is evaluated on a knot projection having $n$ crossings, the result is bounded by a constant times $n^m$. Thus the well known analogy between Vassiliev…

In this paper we give some interesting identities between Euler numbers and zeta functions. Finally we will give the new values of Euler zeta function at positive even integers.

In this paper, we investigate the properties of locally univalent and multivalent planar harmonic mappings. First, we discuss the coefficient estimates and Landau's Theorem for some classes of locally univalent harmonic mappings, and then…