On Equivalent Sublattices of an n-dimensional Lattice

Abstract

This paper investigates the unimodular equivalence of sublattices in an n-dimensional lattice. We introduce a recursive procedure to compute the sizes of these unimodular equivalence classes when the index is a power of a prime p. Additionally, we derive an explicit formula for the number of cocyclic sublattices of a given index m and show that they constitute a single unimodular equivalence class.

Keywords

Lattice / sublattice / the unimodular equivalence / cocyclic sublattices / 11H06 / 20E07 / 52C07

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