Representation of Integers by Form f(x1, x2, x3) Over The Field Δf ,m

Abstract

This paper deals with the representation by the quadratic form in three variables with odd prime invariants. In this paper a primitive quadratic form over the field of integers with odd invariants is considered and another form mutually primitive to it especially for the case m → and the field Δf,m does not change its form. Then it is proved that the number of representations by form is greater than the number of classes of integral primitive binary quadratic forms.