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The prime-component counting conjecture for Apollonian packings
Let ${\mathcal{P}^{\operatorname{full}}}$ be a primitive integral Apollonian packing, and let $C_{{\mathcal{P}^{\operatorname{full}}}}(X)$ be the number of circles of curvature at…
Conjectureopenanalytic-number-theory apollonian-packings prime-componentsarXiv posted 2 days ago
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The growth conjecture for prime and thickened prime components
Let $C_{{\mathcal{P}^{\operatorname{pr}}}}(X)$ be the number of circles of curvature at most $X$ in a prime component ${\mathcal{P}^{\operatorname{pr}}}$ , and let…
Conjectureopenapollonian-packings circle-counting prime-componentsarXiv posted 2 days ago

The prime-component counting conjecture for Apollonian packings