11 research outputs found
Irreducibility criteria for pairs of polynomials whose resultant is a prime number
We use some classical estimates for polynomial roots to provide several
irreducibility criteria for pairs of polynomials with integer coefficients
whose resultant is a prime number, and for some of their linear combinations.
Similar results are then obtained for multivariate polynomials over an
arbitrary field, in a non-Archimedean setting.Comment: 20 page
ON D(-1)- Quadruples
Quadruples (a; b; c; d) of positive integers a < b < c < d with the property that the product of any two of them is one more than a perfect square are studied. Improved lower and upper bounds for the entries b and c are established. As an application of these results, a bound for the number of such quadruples is obtained
Some elementary zero-free regions for Dirichlet series and power series
Adapting some elementary methods used by a number of authors to investigate the location of roots of polynomials with complex coefficients, we present some results which provide zero-free regions for Dirichlet series and power series
ON D(-1)- Quadruples
Quadruples (a; b; c; d) of positive integers a < b < c < d with the property that the product of any two of them is one more than a perfect square are studied. Improved lower and upper bounds for the entries b and c are established. As an application of these results, a bound for the number of such quadruples is obtained
The Irreducibility of Polynomials That Have One Large Coefficient and Take a Prime Value
Irreducibility criteria for compositions of polynomials with integer coefficients
International audienc