Representations of ternary quadratic forms and the class number of imaginary quadratic fields

Thomas Richard Shemanske

Vol. 122 (1986), No. 1, 223–250

DOI: 10.2140/pjm.1986.122.223

Abstract

In this paper, we consider the norm form of a definite rational quaternion algebra restricted to the elements of trace zero in a maximal order of the algebra. When the algebra has class number one, we derive an equation which relates the representation numbers of the norm form to the class number of imaginary quadratic extensions of the rational numbers.

Mathematical Subject Classification 2000

Primary: 11E41

Secondary: 11R29

Milestones

Received: 12 April 1984

Revised: 28 August 1984

Published: 1 March 1986