Arithmetic Properties of Generalized Rikuna Polynomials

Arithmetic Properties of Generalized Euler Numbers

The generalized Euler number En|k counts the number of permutations of {1, 2, . . . , n} which have a descent in position m if and only if m is divisible by k. The classical Euler numbers are the special case when k = 2. In this paper, we study divisibility properties of a q-analog of En|k. In particular, we generalize two theorems of Andrews and Gessel [3] about factors of the q-tangent numbers.

Some new properties of Generalized Bernstein polynomials

Let Bm(f) be the Bernstein polynomial of degree m. The Generalized Bernstein polynomials

The Zagier Polynomials. Part Ii: Arithmetic Properties of Coefficients

Generalized numerical ranges of matrix polynomials

In this paper, we introduce the notions of C-numerical range and C-spectrum of matrix polynomials. Some algebraic and geometrical properties are investigated. We also study the relationship between the C-numerical range of a matrix polynomial and the joint C-numerical range of its coefficients.

Arithmetic Properties of Eigenvalues of Generalized Harper Operators on Graphs

Let Q denote the field of algebraic numbers in C. A discrete group G is said to have the σ-multiplier algebraic eigenvalue property, if for every matrix A ∈ Md(Q(G,σ)), regarded as an operator on l(G), the eigenvalues of A are algebraic numbers, where σ ∈ Z(G,U(Q)) is an algebraic multiplier, and U(Q) denotes the unitary elements of Q. Such operators include the Harper operator and the discrete...