8 problems

For $q=2$, let $X(m,i)$ denote the characteristic-zero variety $X_\infty(m,i)(0)_{c0}$. Its irreducible components are described using rooted weighted binary forests with $i$ nodes…

Let $q=2$. For integers $m$, $i$, and $n\geq 0$, let $X_\infty(m,i)(n)_{c0}\subset \mathbb{P}^{m}(\mathbb{C})$ be the characteristic-zero locus defined by the vanishing of the poly…

Powers-of-coefficients conjecture. For any $i,j,m,n$, there exists $\gamma\in\mathbb{N}$ such that

Let $H_{ij,n}$ be the characteristic-polynomial coefficients from the paper, and let $\gamma$ denote the least exponent in the power-containment conjecture. Gamma-two conjecture. F…

Let $H_{jk}$ be the indicated coefficients in the characteristic-polynomial construction, and let $X(\alpha,i)$ be the corresponding projective variety. Zero-locus conjecture. The…

Let $H_{ij,n}(m)$ and $D(m,i)=H_{i0,0}(m)$ be the polynomials defined by the characteristic-polynomial coefficients above. For $q=2$, let $\langle D(m,0),\dots,D(m,i)\rangle$ denot…

Let $K$ be the rational function field used in the Carlitzian setting, and let $\widehat{\pi}$ be the associated Carlitz period analogue. Transcendence conjecture. The element…

Let $n>0$ and $s\geq 0$ be integers. Write the base-$q$ expansion of $n$ as $n=n_0+n_1q+\cdots+n_rq^r$ and set $\ell_q(n):=\sum_i n_i$. For the finite zeta value of level $s$ and e…