Positive definite binary quadratic forms and modules over a field

Abstract

There has been a connection between binary quadratic forms and modules. Given any quadratic form F, there corresponds a module M-F, and conversely given any module M, there corresponds a binary quadratic form FM. The connection between binary quadratic forms and modules was studied in [3, 4]. In this paper, we consider this connection only for positive definite primitive integral quadratic forms F(x, y) = ax(2)+bxy+cy(2) of discriminant A and modules M over an imaginary quadratic number field F = Q(root Delta).