Derivable quadratic forms and representation numbers

Abstract

Let Fm denote the set of positive-definite primitive integral quadratic forms in m variables. Let f,g∈Fm. In this paper we introduce a new concept, namely that of g being derivable from f. This concept is based on a certain theta function identity being valid. A consequence of this concept is that if g is derivable from f then the representation number of g can be given in terms of that of f. Many examples are given, especially for diagonal ternary quadratic forms.