Published online by Cambridge University Press: 26 February 2010
Let f be a positive-definite ternary quadratic form with integer coefficients; by c(f), the class-number of f, is meant the number of classes in the genus of f. The object of this paper is to find all the f with c(f) = 1; these f are the ones for which , where f′ is an arbitrary ternary form and ∼,
denote equivalence and semi-equivalence respectively. Trivially, it suffices to find the primitive f with c(f) = 1.