AbstractOstrowski established in 1919 that an absolutely irreducible integral polynomial remains absolutely irreducible modulo all sufficiently large prime numbers. We obtain a new lower bound for the size of such primes in terms of the number of integral points in the Newton polytope of the polynomial, significantly improving previous estimates for sparse polynomials
One can associate to any bivariate polynomial P (X,Y) its Newton polygon. This is the convex hull of...
In this note, we show that, for any f ∈ Z[x] and any prime number p, there exists g ∈ Z[x] for which...
AbstractIt is shown that an absolutely irreducible homogeneous cubic polynomialf∈Z[x0, x1, x2] is al...
Abstract. Ostrowski established in 1919 that an absolutely irreducible integral polynomial remains a...
AbstractOstrowski established in 1919 that an absolutely irreducible integral polynomial remains abs...
A multivariable polynomial is associated with a polytope, called its Newton polytope. A polynomial i...
This thesis is a contribution to determine the absolute irreducibility of polynomials via their Newt...
ii Consider a polynomial f(x) having non-negative integer coefficients with f(b) prime for some inte...
Any irreducible polynomial f(x) in [special characters omitted][x] such that the set of values f([sp...
AbstractA multivariable polynomial is associated with a polytope, called its Newton polytope. A poly...
We describe a new method for constructing irreducible polynomials modulo a prime number p. The metho...
We explore two specific connections between prime numbers and polynomials. Cohn\u27s C...
We show that certain problems involving sparse polynomials with integer coefficients are at least as...
In this note, we show that, for any f∈ℤx and any prime number p, there exists g∈ℤx for which the pol...
AbstractWe consider absolutely irreducible polynomialsf∈Z[x, y] with degxf=m, degyf=n, and heightH. ...
One can associate to any bivariate polynomial P (X,Y) its Newton polygon. This is the convex hull of...
In this note, we show that, for any f ∈ Z[x] and any prime number p, there exists g ∈ Z[x] for which...
AbstractIt is shown that an absolutely irreducible homogeneous cubic polynomialf∈Z[x0, x1, x2] is al...
Abstract. Ostrowski established in 1919 that an absolutely irreducible integral polynomial remains a...
AbstractOstrowski established in 1919 that an absolutely irreducible integral polynomial remains abs...
A multivariable polynomial is associated with a polytope, called its Newton polytope. A polynomial i...
This thesis is a contribution to determine the absolute irreducibility of polynomials via their Newt...
ii Consider a polynomial f(x) having non-negative integer coefficients with f(b) prime for some inte...
Any irreducible polynomial f(x) in [special characters omitted][x] such that the set of values f([sp...
AbstractA multivariable polynomial is associated with a polytope, called its Newton polytope. A poly...
We describe a new method for constructing irreducible polynomials modulo a prime number p. The metho...
We explore two specific connections between prime numbers and polynomials. Cohn\u27s C...
We show that certain problems involving sparse polynomials with integer coefficients are at least as...
In this note, we show that, for any f∈ℤx and any prime number p, there exists g∈ℤx for which the pol...
AbstractWe consider absolutely irreducible polynomialsf∈Z[x, y] with degxf=m, degyf=n, and heightH. ...
One can associate to any bivariate polynomial P (X,Y) its Newton polygon. This is the convex hull of...
In this note, we show that, for any f ∈ Z[x] and any prime number p, there exists g ∈ Z[x] for which...
AbstractIt is shown that an absolutely irreducible homogeneous cubic polynomialf∈Z[x0, x1, x2] is al...
DOI
Add to ORKG