3 problems

For integers $k,l,m\ge 2$, define … For $\epsilon>0$ and $0<h\le x^{1-\epsilon}$, the triple convolution conjecture. … as $x\to\infty$, where $\nabla_{h,k,l,m}$ is the explicit Eul…

Let $f=h+\overline{g}\in\mathcal{S}(H_{0})$ satisfy … with dilatation … where $-1<a<1$. Let $f_n=h_n+\overline{g_n}\in\mathcal{S}^{0}(H_{0})$ have dilatation … where…

Let $U$ and $V$ be probability mass functions that are $c$-log-concave with constants $c_U$ and $c_V$, respectively. Write $U\star V$ for their convolution. Convolution conjecture.…