5 problems

Let $Z$ be a torus partition function of the form specified in the source, with at least one chiral current, and let $D(j)$ be the current density satisfying … where $a>0$,…

Modulus-of-continuity conjecture. The modulus of continuity of $\mathsf{\Theta}_{f}(\cdot)$ is the same as the modulus of continuity of $\bm{\chi}$.

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…

Let $S$ be non-decreasing on $[0,infty)$, and suppose that its Laplace-Stieltjes transform satisfies … Assume this function extends analytically to the half-plane…

Type-2 FGV conjecture. The floor-function kernel $\theta(x)=x^{-1}\left\lfloor x\right\rfloor$ and the generalisation $\theta_r$ are conjectured to be FGV of type 2.