On a problem of Tur\'an and sparse polynomials

Abstract: I will give a survey of various results associated with the factorization of sparse polynomials in $\mathbb Z[x]$. One motivating question that pushed some of the results to be considered is a question due to P\'al Tur\'an: Is there an absolute constant $C$ such that if $f(x) \in \mathbb Z[x]$, then there is a polynomial $g(x) \in Z[x]$ that is irreducible and within $C$ of being $f(x)$ in the sense that the sum of the absolute values of the difference $f(x) - g(x)$ is bounded by $C$? This is known to be true as I stated it, but Tur\'an also added the restriction that $\deg g \le \deg f$, and the problem remains open in this case with good evidence that such a $C$ probably does exist.

number theory

Audience: researchers in the topic

Tel Aviv field arithmetic seminar

Series comments: Please sign in to the talk with a full name.

The link to the seminar will be given before the talk in the seminar website www.math.tau.ac.il/~haran/Field-Arithmetic-Seminar/