Some arithmetic aspects of ortho-integral surfaces

Nhat Minh Doan; Khanh Le

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arXiv · 2504.09403

Some arithmetic aspects of ortho-integral surfaces

Nhat Minh Doan·Khanh Le

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Abstract

We investigate ortho-integral (OI) hyperbolic surfaces with totally geodesic boundaries, defined by the property that every orthogeodesic (i.e. a geodesic arc meeting the boundary perpendicularly at both endpoints) has an integer cosh-length. We prove that while only finitely many OI surfaces exist for any fixed topology, infinitely many commensurability classes arise as the topology varies. Moreover, we completely classify OI pants and OI one-holed tori, and show that their doubles are arithmetic surfaces of genus 2 derived from quaternion algebras over $\mathbb{Q}$.

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BibTeX RIS

Nhat Minh Doan, Khanh Le. 2025-04-13. Some arithmetic aspects of ortho-integral surfaces. https://arxiv.org/abs/2504.09403

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