AbstractLet f(X, Y)ϵZ[X, Y] be irreducible. We give a condition that there are only finitely many integers n ϵZsuch that f(n, Y) is reducible and we give a bound for such integers. We prove a similar result for polynomials with coefficients in polynomial rings. Both results are proved by, so-called, nonstandard arithmetic
Given an Hilbertian fieldK, a polynomial g(x) ∈ K[x] and an integer n ∈ N, we show that there exist...
AbstractThe purpose of this article is to get effective information about the following two problems...
AbstractGiven an absolutely irreducible horizontal hypersurface Z in a projective space over the rin...
AbstractWe give sufficient conditions for a sequence of integers to be a Hilbert irreducibility sequ...
AbstractWe prove that if K is a finite extension of Q, P is the set of prime numbers in Z that remai...
AbstractWe characterize the polynomials P(X, Y) that are irreducible over a number field K and such ...
A method for obtaining very precise results along the lines of the Hilbert Irreducibility Theorem is...
In [JM90] Jankowski and Marlewski prove by elementary methods that if f and g are polynomials in Q[X...
AbstractFor polynomials of the form Q = P(f(X), g(Y), where P is a generalized difference polynomial...
AbstractLet K be a field of characteristic 0. We produce families of polynomials f(x,y), irreducible...
Hilbert's irreducibility theorem plays an important role in inverse Galois theory. In this article w...
In its simplest form, the statement of Hilbert's irreducibility theorem says that for an irreducible...
We study abstract algebra and Hilbert's Irreducibility Theorem. We give an exposition of Galois theo...
AbstractLet f(X1,…, Xn) be an absolutely irreducible polynomial with coefficients in a finite field....
We present a simple proof of Königsberg's Criterion, [K] p.69 and also present families of irreducib...
Given an Hilbertian fieldK, a polynomial g(x) ∈ K[x] and an integer n ∈ N, we show that there exist...
AbstractThe purpose of this article is to get effective information about the following two problems...
AbstractGiven an absolutely irreducible horizontal hypersurface Z in a projective space over the rin...
AbstractWe give sufficient conditions for a sequence of integers to be a Hilbert irreducibility sequ...
AbstractWe prove that if K is a finite extension of Q, P is the set of prime numbers in Z that remai...
AbstractWe characterize the polynomials P(X, Y) that are irreducible over a number field K and such ...
A method for obtaining very precise results along the lines of the Hilbert Irreducibility Theorem is...
In [JM90] Jankowski and Marlewski prove by elementary methods that if f and g are polynomials in Q[X...
AbstractFor polynomials of the form Q = P(f(X), g(Y), where P is a generalized difference polynomial...
AbstractLet K be a field of characteristic 0. We produce families of polynomials f(x,y), irreducible...
Hilbert's irreducibility theorem plays an important role in inverse Galois theory. In this article w...
In its simplest form, the statement of Hilbert's irreducibility theorem says that for an irreducible...
We study abstract algebra and Hilbert's Irreducibility Theorem. We give an exposition of Galois theo...
AbstractLet f(X1,…, Xn) be an absolutely irreducible polynomial with coefficients in a finite field....
We present a simple proof of Königsberg's Criterion, [K] p.69 and also present families of irreducib...
Given an Hilbertian fieldK, a polynomial g(x) ∈ K[x] and an integer n ∈ N, we show that there exist...
AbstractThe purpose of this article is to get effective information about the following two problems...
AbstractGiven an absolutely irreducible horizontal hypersurface Z in a projective space over the rin...
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