9 problems

Let $\mathcal{L}$ be the operator governing the steady state in the self-similar variables, and let $\bar{\Omega}$ denote its kernel profile. Let $Ai$ be the Airy function, let…

Products-of-solutions conjecture. The products of the solutions are the independent solutions of a differential equation of order

Let $\beta_n(t,1)$ be the recurrence coefficient associated with the Airy-function determinant at parameter $N=1$, and let $\beta_n'(t,1)$ denote its derivative with respect to $t$…

Let $q_n(z;0)$ denote the Airy solutions indexed by $n\geq 1$, with real variable $z\leq 0$. Clarkson's conjecture. … for every $z\leq 0$ and every $n\geq 1$. This conjecture asser…

Let $a_k$ and $b_k$ be the quantities whose asymptotic expansions are under consideration, and let the $N$th error term mean the error obtained by stopping the corresponding expans…

Let $Upsilon$ be the Airy Riemann–Hilbert problem solution, let $Omega_1$ denote its first sector, and set $xi:=\mathrm{e}^{2pimathrm{i}/3}$. Let $\operatorname{Ai}$ denote the Air…

Convergence conjecture. This condition is sufficient for the series in those cases to converge.

Large-parameter positivity conjecture. There exists $y_1>0$ such that $\delta^T(y)>0$ on $[y_1,+\infty)$. The conjecture concerns the eventual monotonicity of the real part of the…

Upper-bound conjecture. For every positive integer $s$,