Related papers: Polynomially Interpolated Legendre Multiplier Sequ…

It was observed by Bump et al. that Ehrhart polynomials in a special family exhibit properties similar to the Riemann {\zeta} function. The construction was generalized by Matsui et al. to a larger family of reflexive polytopes coming from…

Schinzel's Hypothesis H is a general conjecture in number theory on prime values of polynomials that generalizes, e.g., the twin prime conjecture and Dirichlet's theorem on primes in arithmetic progression. We prove an arithmetic analog of…

In this paper we give a new characterization of simple sets of polynomials B with the property that the set of B-multiplier sequences contains all Q-multiplier sequence for every simple set Q. We characterize sequences of real numbers which…

The problem of interpolation at $(n+1)^2$ points on the unit sphere $\mathbb{S}^2$ by spherical polynomials of degree at most $n$ is proved to have a unique solution for several sets of points. The points are located on a number of circles…

In this paper we study the singularity of multivariate Hermite interpolation of type total degree. We present a method to judge the singularity of the interpolation scheme considered and by the method to be developed, we show that all…

A lemma of Micchelli's, concerning radial polynomials and weighted sums of point evaluations, is shown to hold for arbitrary linear functionals, as is Schaback's more recent extension of this lemma and Schaback's result concerning…

Motivated by the study of the distribution of zeros of generalized Bessel-type functions, the principal goal of this paper is to identify new research directions in the theory of multiplier sequences. The investigations focus on multiplier…

The set A = {a_n} of nonnegative integers is an asymptotic basis of order h if every sufficiently large integer can be represented as the sum of h elements of A. If a_n ~ alpha n^h for some real number alpha > 0, then alpha is called an…

In this paper, we study a class of sequences of polynomials linked to the sequence of Bell polynomials. Some sequences of this class have applications on the theory of hyperbolic differential equations and other sequences generalize…

The main result of this paper is a new version of Newton-Hensel lifting that relates to interpolation questions. It allows one to lift polynomials in $Z[x]$ from information modulo a prime number $p\ne 2$ to a power $p^k$ for any $k$, and…

We establish a lower bound for the frequency with which an irreducible monic cubic polynomial with negative discriminant can be expressed as a sum of two squares ($\square_{2}$). This provides a quantitative answer to a question posed by…

We obtain a series transformation formula involving the classical Hermite polynomials. We then provide a number of applications using appropriate binomial transformations. Several of the new series involve Hermite polynomials and harmonic…

We relate a one-parametric generating function for the squares of Legendre polynomials to an arithmetic hypergeometric series whose parametrisation by a level 7 modular function was recently given by Shaun Cooper. By using this modular…

We prove a classical theorem due to Legendre, about the existence of non trivial solutions of quadratic diophantine equations of the form $ax^2+by^2+cz^2=0$, in the weak fragment of Peano Arithmetic $I\Delta_0+\Omega_1$.

In the paper, the planar polynomial geometric interpolation of data points is revisited. Simple sufficient geometric conditions that imply the existence of the interpolant are derived in general. They require data points to be convex in a…

An analogue of the correspondence between GL(k)-conjugacy classes of matricial polynomials and line bundles is given for K-conjugacy classes, where K is one of the following: maximal parabolic, maximal torus, GL(k-1) embedded diagonally.…

This paper considers the extension of classical Lagrange interpolation in one real or complex variable to "polynomials of one quaternionic variable". To do this we develop some aspects of the theory of such polynomials. We then give a…

H. Lenstra has pointed out that a cubic polynomial of the form (x-a)(x-b)(x-c) + r(x-d)(x-e), where {a,b,c,d,e} is some permutation of {0,1,2,3,4}, is irreducible modulo 5 because every possible linear factor divides one summand but not the…

The binomial interpolated transform of a sequence is a generalization of the well-known binomial transform. We examine a Pascal-like triangle, on which a binomial interpolated transform works between the left and right diagonals, focusing…

In this paper we construct an infinite sequence of binary irreducible polynomials starting from any irreducible polynomial $f_0 \in \F_2 [x]$. If $f_0$ is of degree $n = 2^l \cdot m$, where $m$ is odd and $l$ is a non-negative integer,…