7 problems

A lacunary polynomial is a polynomial with a fixed number of terms, while the degrees and coefficients are unrestricted. Let $f$ and $g$ be polynomials, and consider their composit…

Conjecture B. No polynomial $f\in\mathcal{B}$ has a reciprocal non-cyclotomic component in its factorization.

Asymptotic Reducibility Conjecture. The proportion of polynomials in $\mathcal{B}=\bigcup_{N\geq 2}\mathcal{B}^{(N)}$ which are irreducible is given by a limit, assumed to exist, e…

Let $\mathcal{B}$ be the class of lacunary almost Newman polynomials … where $n\geq 2$, $s\geq 0$, $m_1-n\geq n-1$, and $m_{q+1}-m_q\geq n-1$ for $1\leq q<s$. Asymptotic reducibili…

Asymptotic reducibility conjecture. Assuming the limit exists, the proportion of irreducible polynomials in $\mathcal{B}=\bigcup_{N\geqslant2}\mathcal{B}^{(N)}$ is

Variant Odlyzko–Poonen conjecture. Almost all polynomials in $\mathcal{P}_{-}$ are irreducible; more precisely,

Brown–Dilcher–Manna conjecture. As $n\to\infty$,