5 problems

Let $m,k,n$ be positive integers with $k\geqslant n$, let $f(x_1,\ldots,x_n)\in\mathbb{Q}[x_1,\ldots,x_n]$ be a symmetric polynomial, and let … For the case $m=1$, set…

Let $m$ be a positive integer, let $w\in\mathbb{R}_{>0}^m$ satisfy … and let $v\in\{0,1\}^m$ have independent Bernoulli$(p)$ coordinates, where $0\leq p\leq 1/3$. Weighted Bernoull…

For $n_{1},\dots,n_{d}\in\mathbb{Q}$, define … and let $W_{k}^{\star}(n_{1},\dots,n_{d})$ be the analogous sum with $\zeta_{\mathcal{A}}^{\star}$. For $k,r\in\mathbb{Z}_{\geq1}$ an…

Let $W_{k}(n_{1},\dots,n_{d})$ and $W_{k}^{\star}(n_{1},\dots,n_{d})$ denote the weighted sums of finite multiple zeta values and finite star multiple zeta values, respectively, de…

Define the weighted sums of finite multiple zeta values by … and define $W_{k}^{\star}(n_{1},\dots,n_{d})$ similarly with $\zeta_{\mathcal{A}}^{\star}$ in place of…