The sum of powers as canonical expression

Abstract

1. In this paper I discuss the expression of the general form F of order n, homogeneous in r + 1 variables z0, z1,…, zl,…, zr, as the sum of the nth powers of h + H linear forms in these variables. I take h (> 0) of these linear forms to be undetermined, namely the formswhose coefficients are undetermined; and I take the remaining H(≥0) linear forms to be assigned, namely the formswhose coefficients are assigned.