In mathematics, the Hermite constant, named after Charles Hermite, determines how long a shortest element of a lattice in Euclidean space can be.

.

The square root in the definition of the Hermite constant is a matter of historical convention.

can be defined as the square of the maximal systole-dimensional torus of unit volume.

Examples

The Hermite constant is known in dimensions 1–8 and 24.. This value is attained by the hexagonal lattice of the Eisenstein integers, scaled to have a fundamental parallelogram with unit area.

Estimates

It is known that

A stronger estimate due to Hans Frederick Blichfeldt is

is the gamma function.

See also

• Loewner's torus inequality

• Minkowski's theorem

References