ON THE NUMBER OF REPRESENTATIONS BY POSITIVE-DEFINITE INTEGER-VALUED QUATERNARY QUADRATIC FORMS

Abstract

Let {Q1, Q2, . . . , Qs} be a finite set of positive-definite integer-valued quaternary quadratic forms. We show that there exists a primitive positive-definite integer-valued quaternary quadratic form Q and a positive integer n such that Q represents n more times than Qi for all 1 ≤ i ≤ s.