5 problems

Let $r\in\N$, let $p$ be a prime, and let $\bfs\in\N^d$ satisfy $p>|\bfs|+1$, where $|\bfs|$ is the weight and $Z_{p^r}(\bfs)$ is the corresponding finite Mordell--Tornheim sum. Fi…

The alternating Mordell--Tornheim dimension conjecture. For every $w\geq3$, the space $\AMT_w$ can be generated by $C_w$. The conjecture proposes an explicit family of alternating…

For an index $\boldsymbol{k}=(k_1,\ldots,k_r)\in\mathbb{I}^+$ with $r\neq1$, let $\omega_{\mathcal{A}}(\boldsymbol{k})$ and $\omega_{\mathcal{S}}(\boldsymbol{k})$ be the finite and…

Let $\Omega(\mathbf{k})$ be the real symmetric Mordell–Tornheim value associated with an index $\mathbf{k}\in\mathbb{N}^r$, defined by the limiting construction in the paper. Symme…

Let $\mathcal{Z}$ be the algebra of multiple zeta values, and let $\zeta^{MT}(\mathbf{k};l)$ denote the Mordell–Tornheim multiple zeta value associated with an index $\mathbf{k}$ a…