Arithmetic volumes of indefinite ternary lattices with square free discriminant

TL;DR

This paper provides explicit formulas for the volumes of indefinite ternary lattices with square-free discriminants and verifies these formulas against known cases, enhancing understanding of their geometric properties.

Contribution

It introduces a new explicit formula for the volumes of these lattices and confirms its accuracy through comparison with known fundamental domains.

Findings

Explicit volume formulas for indefinite ternary lattices with square-free discriminant

Validation of formulas through comparison with known fundamental domains

Enhanced understanding of lattice geometric properties

Abstract

The main purpose of this paper is to give an explicit formula for the volumes of indefinite ternary lattices with square free discriminant. We also consider several examples of lattices, for which the fundamental domain is well-known and make sure the results obtained by our computation coincide with the known ones.