12 problems

For each integer $m\geq 0$, define … and … Here an empty sum is understood to be zero. Chen's conjecture. For every integer $m\geq 0$, both $U_m(t)$ and $V_m(t)$ are completely mon…

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…

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…

Let $x,\alpha,\beta$ be parameters, and define … Suppose that $x$ is complex with $\operatorname{Re}(x)>0$, or that either $\alpha$ or $\beta$ is an odd integer, or that…

Resonant-quadruple conjecture. The admissible quadruples are given by either

Conjectural formula for $C_\infty$.

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…

Let $r\in\mathbb{N}$, $v>0$, $m\in\mathbb{N}\cup\\{0\\}$, and $0<\alpha<1$. Define $P_r(\alpha,m,v)$ as the polynomial appearing in the identity below. Polynomial remainder conject…

Let $\psi$ denote the digamma function, and let $\psi'$ and $\psi”$ be its first and second derivatives. For real parameters $\alpha$ and $\beta$, consider $x>0$. The sharp double-…

Let $h_\lambda(x)$ and $h_\mu(x)$ be the functions defined by equation (tetra-square+poly-2), with $x\in(0,\infty)$. The completely monotonic degree of a function is the supremum o…

Let $y>-\frac12$ and let $H_y$ denote the function defined in equation of the source, with parameter $\alpha$, on $x\in(-y-1,\infty)$. A function is logarithmically completely mono…

Conjectured monotonicity of gamma-ratio bounds. The functions at the two ends of these inequalities are perhaps monotonic with respect to $x$ on $(0,\infty)$. The conjecture concer…