14 problems

Todd's dimension conjecture. For every positive integer $w$,

Normal-set representation conjecture. If $S$ is a $p$-normal set, then there exists a field $K$ of characteristic $p$ and a $K$-recurrence sequence $a\in K^{\mathbb N}$ such that

Let multiple zeta values over a polynomial ring in positive characteristic be given by the usual nested sums indexed by compositions. Thakur's one-shuffle conjecture. Multiple zeta…

Let $K$ be the field and let $\Sigma$ be the index set used to define the spaces of multiple polylogarithms and multiple zeta values. Let … be the map obtained by composing the map…

Let $A$ be one of the four class-number-one base rings listed in Examples (i)–(iv), and let $\zeta_A(\mathfrak{s})$ be a multiple zeta value over $A$. A tuple is called Eulerian wh…

Let $q>2$, and let $\zeta_A(\mathfrak{s})$ be a multiple zeta value over $A=\mathbb{F}_q[\theta]$. A tuple $\mathfrak{s}=(s_1,\ldots,s_r)$ is primitive if not all of its entries ar…

Let $k$ be the rational function field underlying the paper, let $v$ be a finite place of $k$, and let $\overline{\mathcal{Z}}$ and $\overline{\mathcal{Z}}_v$ denote the correspond…

Let $\overline{\mathfrak{Z}}$ be the $\overline{\mathbb{Q}}$-algebra generated by multizeta values, and let $\overline{\mathfrak{Z}}_w$ be the $\overline{\mathbb{Q}}$-vector space…

Let $L$ be a field finitely generated over an algebraically closed field $l_0$ of characteristic $p$, and let $C$ be an abelian variety over $L$. For each $\ell\geqslant 0$, choose…

Let $p>0$ be a prime, let $K$ be a field of characteristic $p$, and let $G$ be a subgroup of $K^*\times K^*$ with finite rank … For given $a,b\in K^*$, consider the equation … in…

Let $q=p^l>2$, let $1\leq p^m\leq q$, let $n>0$ and $r\geq 2$, and let $N_i\in \mathbb{N}\cup\{0\}$ for $0\leq i\leq n-1$ satisfy … If … then the displayed multizeta value below is…

For a multizeta value $\zeta_{A}(s_{1},\ldots,s_{r})$ of weight $w:=\sum_{i=1}^{r}s_i$, call it zeta-like if the ratio $\zeta_{A}(s_{1},\ldots,s_{r})/\zeta_{A}(w)$ is algebraic ove…

Let $p$ be a prime, let $f\in \overline{\mathbb{F}}_p(x)$ be a separable rational map, and let $\zeta(f,\mathbb{P}^1(\overline{\mathbb{F}}_p);t)$ denote its Artin–Mazur zeta functi…

Let $K_0$ be the function field of a smooth curve over a finite field ${\Bbb F}$ of characteristic $p$, let $K_0^{\rm s}$ be a separable closure of $K_0$, and let $B$ be an abelian…