Sequences of $\{0,1\}$-polynomials with exponents in arithmetic progression

construction of vector fields with positive lyapunov exponents

in this thesis our aim is to construct vector field in r3 for which the corresponding one-dimensional maps have certain discontinuities. two kinds of vector fields are considered, the first the lorenz vector field, and the second originally introced here. the latter have chaotic behavior and motivate a class of one-parameter families of maps which have positive lyapunov exponents for an open in...

Symbolic Polynomials with Sparse Exponents

Earlier work has presented algorithms to factor and compute GCDs of symbolic Laurent polynomials, that is multivariate polynomials whose exponents are integer-valued polynomials. These earlier algorithms had the problem of high computational complexity in the number of exponent variables and their degree. The present paper solves this problem, presenting a method that preserves the structure of...

The Arithmetic of Borcherds’ Exponents

On orthogonal polynomials related to arithmetic and harmonic sequences

In this paper we study special systems of orthogonal polynomials on the unit circle. More precisely, with a view to the recurrence relations fulfilled by these orthogonal systems, we analyze a link of non-negative arithmetic to harmonic sequences as a main subject. Here, arithmetic sequences appear as coefficients of orthogonal polynomials and harmonic sequences as corresponding Szegő parameters.

On the irreducibility of certain polynomials with coefficients as products of terms in an arithmetic progression

We prove the irreducibility of ceratin polynomials whose coefficients are in arithmetic progression with common difference 2 . We use Sylvester type of results on the greatest prime factor of a product with terms in an arithmetic progression and irreducibility results based on Newton Polygons.