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arXiv · 2609.11398

Reversibility and its asymptotic counting in Picard group

Debattam Das·Krishnendu Gongopadhyay·Anirban Mukhopadhyay
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Abstract

We investigate reversible elements in the Picard modular group $\mathrm{PSL}(2,\mathbb{Z}[i])$. We show that reversibility coincides with strong reversibility for Kleinian groups, in particular for the Picard group. We classify reversible elements in the Picard group and characterize loxodromic reversible elements up to conjugacy. We prove that each such conjugacy class contains exactly eight special representatives. We also obtain asymptotic estimates for the number of reversible conjugacy classes with bounded trace.

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Debattam Das, Krishnendu Gongopadhyay, Anirban Mukhopadhyay. 2026-09-10. Reversibility and its asymptotic counting in Picard group. https://arxiv.org/abs/2609.11398

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