7 problems

Let ${\mathcal{A}}$ be a primitive Apollonian circle packing. Let $S_{\mathcal{A}}$ be the set of missing curvatures that do not lie in any of the quadratic or quartic obstruction…

Let ${\mathcal{A}}$ be a primitive integral Apollonian circle packing. A positive curvature $c$ is missing in ${\mathcal{A}}$ if curvatures congruent to $c$ modulo $24$ occur in…

Let $\mathcal P$ be a primitive integral Apollonian packing, and call an integer a congruence obstruction if it is excluded from occurring as a circle curvature by congruence condi…

Let $\mathcal P$ be a bounded primitive integral Apollonian packing. Define … Here $N_{\mathcal P}(T)$ denotes the relevant circle-counting function. Fuchs–Sanden conjecture. As…

An integer Apollonian circle packing (ACP) is a circle packing whose initial four mutually tangent circles have integer curvatures; in such a packing, all circle curvatures are int…

Kissing-prime counting conjecture. As $x\to\infty$,

Prime-curvature counting conjecture. As $x\to\infty$,