Add to ORKGAbstract. Ostrowski 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. 1
The paper gives a new proof and improvement for the irreducibility of the reduction of a polynomial....
We prove an irreducibility criterion for polynomials with power series coefficients generalizing pre...
AbstractWe characterize the polynomials P(X, Y) that are irreducible over a number field K and such ...
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...
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...
In this note, we show that, for any f∈ℤx and any prime number p, there exists g∈ℤx for which the pol...
This thesis is a contribution to determine the absolute irreducibility of polynomials via their Newt...
We explore two specific connections between prime numbers and polynomials. Cohn\u27s C...
We describe a new method for constructing irreducible polynomials modulo a prime number p. The metho...
In this note, we show that, for any f ∈ Z[x] and any prime number p, there exists g ∈ Z[x] for which...
AbstractWe consider absolutely irreducible polynomialsf∈Z[x, y] with degxf=m, degyf=n, and heightH. ...
We show that certain problems involving sparse polynomials with integer coefficients are at least as...
AbstractIt is shown that an absolutely irreducible homogeneous cubic polynomialf∈Z[x0, x1, x2] is al...
The paper gives a new proof and improvement for the irreducibility of the reduction of a polynomial....
We prove an irreducibility criterion for polynomials with power series coefficients generalizing pre...
AbstractWe characterize the polynomials P(X, Y) that are irreducible over a number field K and such ...
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...
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...
In this note, we show that, for any f∈ℤx and any prime number p, there exists g∈ℤx for which the pol...
This thesis is a contribution to determine the absolute irreducibility of polynomials via their Newt...
We explore two specific connections between prime numbers and polynomials. Cohn\u27s C...
We describe a new method for constructing irreducible polynomials modulo a prime number p. The metho...
In this note, we show that, for any f ∈ Z[x] and any prime number p, there exists g ∈ Z[x] for which...
AbstractWe consider absolutely irreducible polynomialsf∈Z[x, y] with degxf=m, degyf=n, and heightH. ...
We show that certain problems involving sparse polynomials with integer coefficients are at least as...
AbstractIt is shown that an absolutely irreducible homogeneous cubic polynomialf∈Z[x0, x1, x2] is al...
The paper gives a new proof and improvement for the irreducibility of the reduction of a polynomial....
We prove an irreducibility criterion for polynomials with power series coefficients generalizing pre...
AbstractWe characterize the polynomials P(X, Y) that are irreducible over a number field K and such ...