4 problems

Depth-one reduction conjecture. Every derivative sum in the $f_6$ family belongs to the subalgebra of the MZV algebra generated by the single zeta values $\zeta(m)$; no irreducible…

Gamma-product conjecture for the E-determinants. For all non-negative integers $x$ and all $n\geq x$, the three displayed formulas in the source hold:

Let $x,l,n,\eta\in\mathbb{C}$, and define $P$ by … Suppose that $x$ is complex with $\operatorname{Re}(x)>0$, or that either $n$ or $\eta$ is an odd integer, or that $l$ is an even…

For each positive integer $p$, let $c_p,d_p,e_p,f_p,g_p,h_p,i_p,j_p,k_p,l_p$ be the rational coefficients defined by the evaluations of the reciprocal hyperbolic series at $\pi$. C…