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

Irreducibility criteria for compositions of polynomials with integer coefficients

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