关于实二次型 a(X^2+3y^2)+bz^2表数相同的问题

A Problem of the Forms a(x^2+3y^2)+bz^2 Representing the Same Numbers

本文证明了形如a(x^2+3y^2)+bz^2(0<3a≤b)的实二次型在整数环上等价的充分必要条件为:对变元的整数值,表数相同。

In this paper,let f and F to be two positive definite real ternaryquadratic forms of the type α(x^2+3y^2)+bz^2(0<3α<b).Then,the formsf and F represent the same numbers for all integral values of theirvariables if and only if f is identical with F.