240 problems

Generating-function conjecture. The dimensions of these spaces satisfy

Let ${\cal FC}$ be the algebra of formal cell-zeta numbers, let $\zeta_2$ be the element whose period is $\zeta(2)$, and let $\widehat{\mathcal{M}}(\mathbb Z)$ denote the completed…

Three-block symmetry conjecture. For any non-negative integers $a_1,a_2,a_3,b_1,b_2$,

Let $A=3$ and let $n\geq 0$ be an integer. Define … For a polynomial $P(K_1,K_2,K_3)$ in any of the four families specified in Theorem … sum{k1geq k2geq k3geq 1}frac{P(K1,K2,K3)}{(…

Let $n\geq 0$ be an integer. Let $\sigma\in\{2,3\}$ be the element satisfying $\sigma\equiv n\pmod 2$, and let $\widetilde{\sigma}$ be the other element of $\{2,3\}$. Let…

Define the multiple zeta values by … for $s_1\geq 2$ and $s_2,\ldots,s_p\geq 1$. Selected-value independence conjecture. Among the numbers $1$, $\zeta(2)$, $\zeta(3)$, $\zeta(2,3)$…

Define the multiple zeta values by … for $s_1\geq 2$ and $s_2,\ldots,s_p\geq 1$. Low-depth independence conjecture. Among the numbers $1$, $\zeta(2)$, $\zeta(3)$, and…

Let ${\cal Z}^{\cal H}_{\bullet}$ be the graded Hopf algebra of framed Hodge-Tate structures generated by the Hodge multiple-zeta structures, and let…

Let ${\cal Z}$ be the commutative algebra over $\mathbb Q$ spanned by multiple zeta values, and let ${\cal Z}_k$ denote its weight-$k$ subspace. Let ${\cal F}(3,5,...)_{\bullet}$ b…

Let the multiple zeta values be the coefficients associated with the Drinfel'd associator, and let Property II refer to the listed relations of that associator, denoted in the sour…

For each natural number $w$, let $Z_w$ be the $\mathbb Q$-vector space generated by multiple zeta values of weight $w$, let $Z_0=\mathbb Q$, and let…

Let $\mathfrak D_\bullet=\bigoplus_{w>2}\mathfrak D_w$ be the stable derivation algebra, a filtered graded Lie algebra over $\mathbb Q$. The conjecture concerns its generators in t…

For weight $n$ and depth $k$, let $P(n,k)$ denote the number of irreducible multiple Clausen values such that a rational basis at that weight and depth is formed from a minimum num…

Depth-one reduction conjecture. Every derivative sum in the $f_6$ family belongs to the subalgebra of the MZV algebra generated by the single zeta values $\zeta(m)$; no irreducible…

Let $M(\bs;\varepsilon)$ denote a multiple mixed value and $T(\bs)$ a multiple t-value. Classify indices as wide, slender, or narrow according to whether their largest component is…

Let $M(\bs;\varepsilon)$ denote a multiple mixed value and $T(\bs)$ a multiple t-value. Classify indices as wide, slender, or narrow according to whether their largest component is…

Let $M(\bs;\varepsilon)$ denote a multiple mixed value of depth $4$, let $T(\bs)$ denote a multiple t-value, and classify indices as wide, slender, or narrow by whether their large…

Let $\bfs$ be an index, let $T(\bfs)$ be a multiple t-value (MTV), and let $\bfs^*$ be its dual. Define the width $\operatorname{wth}(\bfs)$ as the largest component of $\bfs$; cal…

Let $d$ be a positive integer with $d\ge 3$. Write $1_{d-3}$ for a string of $d-3$ entries equal to $1$, let $\zeta^\sharp$ denote the Euler sharp sum, and let $\zeta(m,n)$ denote…

Kaneko–Zagier conjecture. There exists an isomorphism

Let $s$ satisfy $\operatorname{Re}(s)>1$, and let $(k_1,\ldots,k_p)$ and $(l_1,\ldots,l_q)$ be distinct finite sequences of positive integers. Write $H_s^\star(k_1,\ldots,k_p)$ for…

Zero-measure conjecture.

No-interior conjecture. For every $p\geq 2$ and every $a,b\in\mathbb{R}$,

Integral algebraicity conjecture. For every integer $q\geq 2$,

Algebraicity conjecture.