THE BASE POINTS OF INDEFINITE QUADRATIC FORMS IN THE CYCLE AND PROPER CYCLE OF AN INDEFINITE QUADRATIC FORM

Abstract

Let F = (a, b, c) be an indefinite quadratic form of discriminant ∆ > 0.In the first section, we give some preliminaries from binary quadraticforms. In the second section, we derive some results concerning thebase points of indefinite quadratic forms in the cycle and proper cycleof F using the transformations τ (F) = (−a, b, −c), ξ(F) = (c, b, a),χ(F) = (−c, b, −a), ψ(F) = (−a, −b, −c), and the right neighbor Ri(F)of F for i ≥ 0.