5 problems

Let $\mathcal{L}^{o}_{k}$ and $\mathcal{L}^{e}_{k}$ denote the spaces of iterated log-sine integrals at $\pi/3$ of weight $k$ with odd and even…

For $k,d\in\mathbb{Z}_{\geq 0}$, define … … Let $\mathcal{C}_k$ and $\mathcal{G}_k$ be the spaces spanned by multiple Clausen and multiple Glaisher values of weight $k$, respective…

Shifted log-sine basis conjecture. The set of real numbers $S'_{k,k}$ is a basis of $\mathcal{Z}_{k}$. If true, this would imply Zagier's dimension conjecture for multiple zeta val…

For $k\in\mathbb{Z}_{\geq 0}$ and $d\in\mathbb{Z}_{\geq 0}$, let … and let a multiple zeta value have weight $k$ and depth $d$. Generation conjecture. Every multiple zeta value wit…

Let $\operatorname{SLs}(k_{1},\dots,k_{n})$ denote a shifted log-sine integral, with $m,n\geq 0$ and $k_i\geq 2$. Linear-independence conjecture. The elements of … are $\mathbb{Q}$…