All Questions

I would like to see criteria for the irreducibility of a polynomial over $\mathbb{Z}$ based (mainly) on the location of the roots of the polynomial in the complex plane. An example of such a criterion ...

As increasingly higher degree terms are added to a "random" polynomial, the roots of a polynomial can be proven to approach the unit circle. For example, see the MathOverflow question Why ...

Let $p(z) = \prod_{j=1}^{l+1} (z - z_j)^{M_j}$ be a complex polynomial of degree $n$, where the $z_j$ are distinct for $1, \ldots, l+1$. The first $l$ entries in the list $\{z'_1, \ldots, z'_{n-1} \}$ ...

There is an Appell sequence of polynomials $p_n(z)$ related to an infinitesimal generator for one rep of the fractional calculus that have coefficients involving the Riemann zeta function values at ...

In past days I was trying to create problems or direct applications invoking Eneström—Kakeya and Gauss-Lucas theorems for certain arithmetic functions that I know from analytic number theory. These ...