Random lattices and n mod 1 Gaps for random points 1 0.8 0.6 - PDF document

Dec 08, 2022 •477 likes •591 views

Random lattices and n mod 1 Gaps for random points 1 0.8 0.6 0.4 0.2 0.5 1 1.5 2 2.5 Gaps for n mod 1 1.0 6/ 2 0.5 0.0 0.0 0.5 1.0 1.5 2.0 The space of lattices Geodesic for 2 1 / 3 pics/CubeRoot_2 : 200

Random lattices and √ n mod 1
Gaps for random points 1 0.8 0.6 0.4 0.2 0.5 1 1.5 2 2.5
Gaps for √ n mod 1 1.0 6/ π 2 0.5 0.0 0.0 0.5 1.0 1.5 2.0
The space of lattices
Geodesic for 2 1 / 3 pics/CubeRoot_2 : 200
√ Geodesic for 12 pics/2_Sqrt_3 : 20
Geodesic for 2 e pics/2E : 200
Closed horocycles
Horocycles centered at a cusp pics/Horo1 : 6 pics/Horo4 : 24 pics/Horo8 : 48 pics/Horo16 : 100
Long horocycles pics/Horo32 : 200 pics/Horo64 : 400 pics/Horo256 : 1600 pics/Horo128 : 800

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