11 problems

Let $\overline{a}(n)$ denote the cubic overpartition function, and define its Jensen polynomials by … For each degree $d$, let $N_{\overline{a}}(d)$ be the minimum integer such tha…

Let $a,b>0$ and $r\in(0,1)$. Let $\Lambda(a,r)$ and $\Lambda_2(a,b_1,b_2,r)$ denote the quantities defined earlier in the source by the inequalities referenced as … , respectively.…

Let $F(a,b;c;r)={}_2F_1(a,b;c;r)$ denote the Gaussian hypergeometric function, defined for the parameters under consideration by … For $a>0$, $b>0$, and $r\in(0,1)$, consider the r…

Craig–Pun's conjecture. The function $q(n)$ is log-concave for $n\geq33$ and satisfies the higher-order Turán inequalities for $n\geq121$.

Heim–Neuhauser–Tröger's conjecture. The function $\mathrm{PL}(n)$ is log-concave for every integer $n\geq 12$.

First Hankel relaxation Riemann hypothesis.

Let $\{\gamma_i\}_{i\geq 0}$ be a shifted multiplier sequence that is eventually increasing, and define … The Turán-transform preservation conjecture. For every $j\in\mathbb{N}$, t…

Let $\{\gamma_i\}_{i\geq 0}$ be a shifted multiplier sequence that is eventually increasing. For $j\in\mathbb{N}$, let $T_j$ denote the order-$j$ Turán operator, and write…

Higher-order partition-function inequality. For $n\geq 2$,

For $x\in(0,1)$ fixed, let $p\mapsto {\rm arcsinh}_p(x)$ denote the generalized inverse hyperbolic sine as a function of $p$. Concavity conjecture. The function…

Bessel-function conjecture. The equation $\Phi_\nu'(x)=0$ has infinitely many roots, with