Zeta functions enumerating subforms of quadratic forms
Number Theory
2024-09-10 v1
Abstract
In this paper, we introduce and study the Dirichlet series enumerating (proper) equivalence classes of full rank subforms/sublattices of a given quadratic form/lattice, focusing on the positive definite binary case. We obtain formulas linking this Dirichlet series with Dirichlet series counting ideal classes of the imaginary quadratic field associated with the quadratic form. Utilizing the result, we provide explicit formulas of the Dirichlet series for several lattices, including square lattice and hexagonal lattice. Moreover, we investigate some analytic properties of this Dirichlet series.
Cite
@article{arxiv.2409.05625,
title = {Zeta functions enumerating subforms of quadratic forms},
author = {Daejun Kim and Seok Hyeong Lee and Seungjai Lee},
journal= {arXiv preprint arXiv:2409.05625},
year = {2024}
}
Comments
37 pages