On the representation of integers with large square factors by positive definite ternary quadratic forms

Abstract

It is proved here that, if G is a positive definite integral ternary quadratic lattice of discriminant d and c is a squarefree integer which is primitively represented by the genus of G , then G primitively represents all sufficiently large integers of the type ct 2 , with g.c.d. ( t , 2 d ) = 1, which are primitively represented by the spinor genus of G .