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arXiv · 2505.00484

Zeta functions of quadratic lattices of a hyperbolic plane

Daejun Kim·Seok Hyeong Lee·Seungjai Lee
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Abstract

In this paper, we study the Dirichlet series that enumerates proper equivalence classes of full-rank sublattices of a given quadratic lattice in a hyperbolic plane -- that is, a nondegenerate isotropic quadratic space of dimension $2$. We derive explicit formulas for the associated zeta functions and obtain a combinatorial way to compute them. Their analytic properties lead to the intriguing consequence that a large proportion of proper classes are one-lattice classes.

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Daejun Kim, Seok Hyeong Lee, Seungjai Lee. 2025-05-01. Zeta functions of quadratic lattices of a hyperbolic plane. https://arxiv.org/abs/2505.00484

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