Classical lattice

Covolume of a classical lattice

Let 𝐿 ≤ℤℝ𝑛 be a complete classical lattice. The covolume of 𝐿 is the measure of the Fundamental domain, geo or equivalently

covol⁡(𝐿)=vol⁡(ℝ𝑛/𝐿)

where vol is an induced measure.

Properties

1. Suppose 𝐿′ ≤ℤ𝐿 is a complete sublattice. Then covol⁡(𝐿′) =|𝐿/𝐿′|covol⁡(𝐿).

Proof

proof

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