3 problems

Let $x_1,\ldots,x_r$ be roots of unity, let $a\in\mathbb{C}\setminus\mathbb{Z}$, and let $\bfk=(k_1,\ldots,k_r)\in\mathbb{N}^r$ satisfy $(k_1,x_1)\neq(1,1)$ and…

Parametric Euler-sum conjecture. These sums can be evaluated in terms of Hurwitz zeta values and digamma functions. This extends the preceding explicitly known cases, but the sourc…

Let $s_1$ and $s_2$ be rational numbers between $0$ and $1$, and let … where $\zeta(s,a)=\sum_{n=0}^{\infty}(n+a)^{-s}$ is the Hurwitz zeta function. The integrality conjecture for…