Definition:Hermite Constant

Definition
Let $n \in \N$ be a natural number.

Let $L$ be an integer lattice in Euclidean space $R^n$ unit covolume.

That is:
 * $\map {\operatorname {vol} } {\dfrac {R^n} L} = 1$

Let $\map {\lambda_1} L$ denote the least length of a nonzero element of $L$.

Let $\sqrt {\gamma_n}$ be the maximum of $\map {\lambda_1} L$ over all such integer lattices $L$.

The Hermite constant of dimension $n$ is the constant $\gamma_n$.