چکیده (انگلیسی):

Let fbe a positive definite ternary quadratic form. We assume that fis non-classic integral, that is, the norm ideal of fis Z. We say fis strongly s-regularif the number of representations of squares of integers by fsatisfies the condition in Cooper and Lam’s conjecture in [3]. In this article, we prove that there are only finitely many strongly s-regular ternary forms up to isometry if the minimum of the nonzerosquares that are represented by the form is fixed. In particular, we show that there are exactly 207non-classic integral strongly s-regular ternary forms that represent one (see Tables 1 and 2). This result might be considered as a complete answer to a natural extension of Cooper and Lam’s conjecture.