11 problems

Let $B_1,\ldots,B_k\subset\mathbb Z^1_{\geqslant 0}$ be support sets, let $d_i:=\min B_i>0$, and let … Assume that $j_\infty=1$, equivalently that the associated map germ is inject…

Let $f_{2^k,n}$ denote the sequence of values defined in the paper, and let $k\geq 1$ and $\nu\geq 0$ be integers. For each interval of integers … consider the signed sequence…

Let $f_n(z)=f_{2,n}(z)$, and for a sequence $(a_n)$ define the operator … A sequence is called $k$-log-concave when $\mathcal L^j(a_n)\geq 0$ for $j=0,1,\ldots,k$, and infinite log…

Let $p$ and $t$ be fixed, and let $f\in\mathbb{Z}[x_1]$ be an input $t$-nomial, meaning a univariate integer polynomial with at most $t$ monomial terms. Root-counting conjecture. T…

Let an extremal reciprocal primitive be an extremal reciprocal algebraic integer that is primitive, and let an octanomial be a polynomial with eight nonzero monomials. Octanomial e…

Schinzel's non-cyclotomic factorization conjecture. There are finite sets $\Omega^0\subset\mathbb{Z}^{n\times n}$ of nonsingular matrices and $\Gamma\subset\mathbb{Z}^n$ of nonzero…

Schinzel's factorization conjecture. There is a finite set of matrices $\Omega\subset\mathbb{Z}^{n\times n}$ such that, for each ${\boldsymbol{a}}\in\mathbb{Z}^n$, there are…

Factorial decay conjecture. There exists a constant $\gamma>0$ such that

Polylogarithmic root-bound conjecture. There is an absolute constant $c\geq 1$ such that this trinomial has no more than $(\log p)^c$ roots in $\mathbb{F}_p$.

For $f\in\mathbb{Z}[x_1]$, let $\tau(f)$ denote its number of nonzero coefficients, and let the roots of $f$ be counted in the indicated fields. Adelic Tau conjecture. There is…

For a prime $p$, let ${\mathcal F}^*_{n,n+1}$ denote the class of $(n+1)$-nomials in $n$ variables, and let ${\text{{\tt FEAS}}}_{\mathbb{Q}_p}$ be the feasibility problem for rati…