3 problems

Partition-function Jensen-polynomial conjecture. For every positive integer $m\geq 4$, there exists a positive integer $N(m)$ such that, for every $n\geq N(m)$, the polynomial…

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

Let $p(n)$ denote the number of partitions of $n$. Desalvo–Pak's conjecture. For every integer $n\geq45$, … The coefficient $\frac{\pi}{\sqrt{24}}$ is asymptotically best possible,…