Reducibility of polynomials of the form f(x)-g(y)
Regular Sequences of Symmetric Polynomials
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
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
Simples remarques sur les racines entières des équations cubiques
Single polynomials that correspond to pairs of cyclotomic polynomials with interlacing zeros
We give a complete classification of all pairs of cyclotomic polynomials whose zeros interlace on the unit circle, making explicit a result essentially contained in work of Beukers and Heckman. We show that each such pair corresponds to a single polynomial from a certain special class of integer polynomials, the 2-reciprocal discbionic polynomials. We also show that each such pair also corresponds (in four different ways) to a single Pisot polynomial from a certain restricted class, the cyclogenic...
Small limit points of Mahler's measure.
Some classes of irreducible polynomials
Sommes de carrés de polynômes irréductibles dans
Specializations of one-parameter families of polynomials
Let be a number field, and suppose is irreducible over . Using algebraic geometry and group theory, we describe conditions under which the -exceptional set of , i.e. the set of for which the specialized polynomial is -reducible, is finite. We give three applications of the methods we develop. First, we show that for any fixed , all but finitely many -specializations of the degree generalized Laguerre polynomial are -irreducible and have Galois group . Second, we study specializations...
Squarefree values of polynomials all of whose coefficients are 0 and 1
Strong Riesz sets and polynomials
Sums of k-th powers in the ring of polynomials with integer coefficients
Sur la distribution modulo M des suites polynomiales [P(n)].