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Toshiki Matsusaka

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Preprint Sep 2026

Distribution of Kaneko's val function

Kaneko's val function is defined as the normalized cycle integral of the elliptic modular $j$-function along closed geodesics on the modular surface. We prove that, when primitive hyperbolic conjugacy classes are ordered by geodesic length, its values concentrate at the single point 720. More generally, an analogous co...

Toshiki Matsusaka · 0 citations