11 problems

Laplace-transform criterion. The function $L_m$ is the Laplace transform of some random variable if and only if $m=0$, corresponding to a trivial random variable, or $m\ge e$.

The ratio refers to the ratio of Laplace transforms of powers of a function, as studied in the identification problem for functions arising in empirical auctions. A function is càd…

Conjecture. If $f$ is $m$-times differentiable at $x_0>0$, then

Finite Laplace transform question. Can the finite Laplace transform of this function be expressed in terms of the Fox H-function?

Let $F$ be a cumulative distribution function, and let $K(F,\cdot)$ be the function defined in the auction-theoretic setting of the paper. Injectivity conjecture. The map … remains…

Gukov–Mariño–Putrov conjecture. The $q$-series of the surgered manifold is obtained by

Let $\mathcal{P}_{\bm{t}}$ and $\bm{V}_s$ be as in Proposition. For a coordinate $k$, define the moment … Let $\Delta$, $\boldsymbol{\lambda}$, and the inverse Laplace operators…

Let $\mathcal{S}_p=\operatorname{Sym}(\mathbf{R},p)$ be the space of symmetric $p\times p$ matrices, let $\mathcal{S}_p^+$ be the open cone of positive definite matrices, and let…

Polynomial-form conjecture. This integral is of the form

Let ${\mathcal M}$ be the subspace of polynomials $f(\xi,z)\in{\mathbb C}[\xi,z]$ such that ${\mathcal Z}(f)$ has no holomorphic part, equivalently such that the Laplace transforma…

Let $(X^{(\alpha)}_t)_{t\in[0,T)}$ be the diffusion considered in the paper, and let the joint Laplace transform in Theorem described in the source be the explicit formula for the…