13 problems

Periods in this setting have algebraic relations, and motivic relations provide the corresponding algebraic framework. Grothendieck's period conjecture. The relations between perio…

Let $q$ be a power of $2$, and let $0\leq i\leq2$ and $0\leq j\leq2-i$. Define … For $a\in\{4q,q^2+q-1,q^2+q,q^2+2q-2,q^2+2q-1,q^2+2q\}$, the two-term relation conjecture asserts ……

Let $\zeta(s_1,\ldots,s_r)$ be a multizeta value over the rational function field, and call it Eulerian when it is a rational multiple of $\widetilde{\pi}^{\sum_i s_i}$. Eulerian m…

The class-number-one zetalike conjecture. The multizeta values

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 $q=p^l>2$, 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 $q$ be a prime power, and let $[i]$ and $\ell_i$ denote the standard Carlitz factorial factors used in the source. Conjectural zeta-like families. The following identities are…

Let $q=2$, and consider primitive tuples of depth $2$. Depth-two classification conjecture for q=2. The zeta-like, equivalently eulerian, primitive tuples are exactly … The source…

Let $q$ be a prime power, and consider primitive tuples of depth $2$ and weight at most $q^2$. Depth-two classification conjecture. The zeta-like primitive tuples are exactly … whe…

Let $p$ be the characteristic, let $q$ be the size of the finite field, and let a tuple have depth $r$. Its weight is the sum of its components; call a tuple primitive when it is n…

Splicing conjecture. If this total weight is a power of $2$ or one less than a power of $2$, then $(s_1,\dotsc,s_r)$ is zeta-like, except when the two tuples being spliced are…

Let $(s_1,\dotsc,s_r)$ be a tuple of positive integers, and call it zeta-like when its associated multizeta value is zeta-like; call a tuple eulerian when its associated multizeta…