Classification of the sublattices of a lattice

Abstract

In 1945-46, C. L. Siegel proved that an $n$-dimensional lattice $\Lambda$ of determinant $\det (\Lambda )$ has at most $m^{n^2}$ different sublattices of determinant $m\cdot \det (\Lambda )$. In 1997, the exact number of the different sublattices of index $m$ was determined by Baake. This paper presents a systematic treatment for counting the sublattices and deduces a formula for the number of the sublattice classes of determinant $m\cdot \det (\Lambda )$.

8 pages

References in corpus (1)

• Similar sublattices of planar lattices

Cited by in corpus (1)

• Maximal root subsystems of affine reflection systems and duality