Abstract:Let $\Gamma$ be a Zariski dense Anosov subgroup of a connected semisimple real algebraic group -- these are higher rank analogues of convex cocompact subgroups. Let us measure the Jordan projections with any linear form which is positive on the limit cone of $\Gamma$. We prove a corresponding counting theorem with a power saving error term for the conjugacy classes of loxodromic elements in $\Gamma$. The proof is based on interpreting the Jordan projections as periods of a natural flow associated to $\Gamma$ and proving exponential mixing. We also prove the existence of a spectral gap for the Selberg zeta function.
From: Pratyush Sarkar [view email]
[v1]
Wed, 21 Aug 2024 01:56:16 UTC (56 KB)
[v2]
Fri, 21 Feb 2025 20:23:45 UTC (59 KB)
[v3]
Wed, 17 Jun 2026 00:58:15 UTC (64 KB)
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