14 problems

Let $\mathcal{Z}_q$ be the algebra of balanced multiple $q$-zeta values, generated by elements $\zeta_q(s_1,\ldots,s_l)$ with $s_1\geq1$ and $s_2,\ldots,s_l\geq0$. The balanced qua…

Balanced multiple q-zeta relation conjecture. All algebraic relations in $\mathcal{Z}_q$ are induced by the balanced quasi-shuffle product and the $\tau$-invariance of balanced mul…

Let $\mathfrak{bm}_0$ be the balanced multiple $q$-zeta Lie algebra candidate and let $\operatorname{gr}_D\mathfrak{bm}_0$ be its associated depth-graded Lie algebra. Write … for i…

Let $\mathfrak{bm}_0$ be the Lie algebra candidate defined by the balanced quasi-shuffle primitiveness and $\tau$-invariance conditions, let $\mathfrak{lq}$ be the ambient Lie alge…

Let $\mathfrak{bm}_0$ be the space of all $\Phi\in\mathbb{Q}\langle\mathcal{B}\rangle$ satisfying $(\Phi\mid b_0)=0$, $(\Phi\mid b_k)=0$ for $k=2,4,6$, primitiveness for the balanc…

Let $\mathcal{B}=\{b_i\mid i\geq0\}$ and let $\mathbb{Q}\langle\mathcal{B}\rangle^0$ be the subspace spanned by words that do not end in $b_0$. The balanced quasi-shuffle product i…

Let $\mathcal{Z}_q$ be the $\mathbb{Q}$-algebra spanned by Schlesinger–Zudilin multiple $q$-zeta values. The Bachmann spanning conjecture. The brackets are enough to span…

Let $\mathcal{Z}_q$ be the $\mathbb{Q}$-algebra spanned by Schlesinger–Zudilin multiple $q$-zeta values … The stuffle–tau conjecture. All algebraic relations in $\mathcal{Z}_q$ are…

Let $\mathcal{Z}_q$ be the algebra of multiple $q$-zeta values, and let $\zeta_q(k_1,\ldots,k_d)$ denote the corresponding multiple $q$-zeta values for indices…

Let $\mathcal{Z}_q$ be the algebra of multiple $q$-zeta values, and let the combinatorial bi-multiple Eisenstein series $G\binom{k_1,\ldots,k_d}{m_1,\ldots,m_d}$ form a spanning se…

Let $q$ be the formal variable and let $\mathcal{Z}_q$ denote the algebra of multiple $q$-zeta values, namely the $\mathbb{Q}$-subalgebra of $\mathbb{Q}\llbracket q\rrbracket$ span…

Three-dimensional qMZV conjecture. Connected generating functions satisfy

Hilbert-scheme qMZV conjecture. The series $\langle f\rangle'$ is a multiple $q$-zeta value of the same weight as $f$, where

qMZV algebra conjecture. The algebra $\mathsf{qMZV}$ is spanned by the series $Z(\mathsf{s})$ with $2\leq s_i\leq 5$, is $\mathbb{Z}/2$-graded by weight, and is stable under…