Published online by Cambridge University Press: 24 October 2008
Let f = f(x1, …, xn) be a positive definite quadratic form in n ( ≤ 8) variables; then we consider the old problem of estimating the minimum of f (its least value for integers xi not all 0) in terms of the determinant Δ(f). Normalizing by supposing the minimum to be 1, the known results may be stated as
each inequality being best possible. Further, for each n, all forms for which equality holds in (1) have integral coefficients and are equivalent to each other.