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math.NT2023★ 8 cited
The local-global conjecture for Apollonian circle packings is false
Summer Haag, Clyde Kertzer, James Rickards +1
In a primitive integral Apollonian circle packing, the curvatures that appear must fall into one of six or eight residue classes modulo 24. The local-global conjecture states that…
math.DS2023
Linking number of modular knots
James Rickards
We compute the linking number of two modular knots in the space with the trefoil filled in, which answers a question…