Prime values of irreducible polynomials
Prime values of reducible polynomials, I
Prime values of reducible polynomials, II
Primteiler von Polynomen.
Proof of a determinant evaluation conjectured by Bombieri, Hunt and van Poorten.
Reducibility and irreducibility of Stern -polynomials
The classical Stern sequence was extended by K.B. Stolarsky and the first author to the Stern polynomials defined by , , , and ; these polynomials are Newman polynomials, i.e., they have only 0 and 1 as coefficients. In this paper we prove numerous reducibility and irreducibility properties of these polynomials, and we show that cyclotomic polynomials play an important role as factors. We also prove several related results, such as the fact that can only have simple zeros, and we state a...
Reducibility of lacunary polynomials II
Reducibility of lacunary polynomials, VI
Reducibility of polynomials of the form f(x)-g(y)
Regular Sequences of Symmetric Polynomials
Remarque sur un théorème de M. A. Pellissier
Representations of multivariate polynomials by sums of univariate polynomials in linear forms
The paper is concentrated on two issues: presentation of a multivariate polynomial over a field K, not necessarily algebraically closed, as a sum of univariate polynomials in linear forms defined over K, and presentation of a form, in particular a zero form, as the sum of powers of linear forms projectively distinct defined over an algebraically closed field. An upper bound on the number of summands in presentations of all (not only generic) polynomials and forms of a given number of variables and...
Restricted sums in a field
Riordan arrays, orthogonal polynomials as moments, and Hankel transforms.
Root separation for reducible integer polynomials
We construct parametric families of (monic) reducible polynomials having two roots very close to each other.
Root separation for reducible monic quartics
Root systems and the Erdős-Szekeres Problem
Schinzel's problem: Imprimitive covers and the monodromy method
Sharper ABC-based bounds for congruent polynomials
Agrawal, Kayal, and Saxena recently introduced a new method of proving that an integer is prime. The speed of the Agrawal-Kayal-Saxena method depends on proven lower bounds for the size of the multiplicative semigroup generated by several polynomials modulo another polynomial . Voloch pointed out an application of the Stothers-Mason ABC theorem in this context: under mild assumptions, distinct polynomials of degree at most cannot all be congruent modulo . This paper presents two improvements...
Simples remarques sur les racines entières des équations cubiques