14 problems

Conjecture for $\mathcal Z_2$. For $1/2<\sigma\leq 1$ and $t\geq t_0>0$, one has

The authors' conjecture.

Let $I_{\lambda_0,f}(\lambda)$ denote the Mellin transform associated with the parameters $\lambda_0$, $f$, and $\lambda$, and let $q$ be the residue-field cardinality. Rationality…

Let $m$ be a positive integer, let $g$ be a function satisfying suitable growth conditions, and define polynomials by … For a function $g$, write…

Mellin–Barnes integrals conjecture. Certain linear combinations of the $J_w$ functions, in particular the $K_w$ function, can be represented by Mellin–Barnes integrals whose contou…

Conjecture E. When $H_s$ is defined by $(0.2)$, $L(s,\pi)=0$, and $\mathcal{M}H_s$ is defined,

Let $H_{4,4}^{2,2}(k,\alpha;r/s)$ be the kernel associated with the Mellin multiplier $\mathcal H_{4,4}^{2,2}(k,\alpha;z)$, with $r$ and $s$ radial variables and $k,n$ the indices…

Let $U\subset X$ be complex manifolds satisfying the conditions in Theorem. Let $\mathcal F\in D^b_c(X,A)$ be a constructible complex such that $\mathcal F|_U\neq 0$. Non-vanishing…

Let $S$ be a non-negative non-decreasing function whose Mellin transform … after subtraction of the pole term $A/(s-1)$ admits an analytic extension to a half-plane…

Self-duality conjecture. Under $\tau\mapsto1/\tau$ and $q\mapsto q/\tau$, it satisfies

Let … and define $M_{\widehat f}$ analogously for the Fourier transform $\widehat f$. Normalize the limiting functions by $f(0)=\widehat f(0)=1$. Mellin midpoint-value conjecture.…

Let $\dot{R}(x)$ be the Riesz function, let $T$ be a suitable test function with Mellin transform $\bar{T}(s)$ existing in the region $\frac{1}{2}+\eta\leq\Re(s)\leq2-\eta$ for…

Let the completed diagram be obtained by completing the external structure of the relevant Feynman diagram, and let a cube mean a fully symmetric parametric integration domain and…

Natural-boundary conjecture. The analytic continuation of $\mathcal{Z}_3(s)\equiv\mathcal{M}_6(s)$ has