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Zeta functions of quadratic lattices of a hyperbolic plane

Author

Listed:
  • Daejun Kim
  • Seok Hyeong Lee
  • Seungjai Lee

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.

Suggested Citation

  • Daejun Kim & Seok Hyeong Lee & Seungjai Lee, 2026. "Zeta functions of quadratic lattices of a hyperbolic plane," Mathematische Nachrichten, Wiley Blackwell, vol. 299(1), pages 290-311, January.
    • Handle: RePEc:bla:mathna:v:299:y:2026:i:1:p:290-311
    DOI: 10.1002/mana.70102
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