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 Delta > 0. In the first section, we give some preliminaries from binary quadratic forms. In the second section, we derive some results concerning the base points of indefinite quadratic forms in the cycle and proper cycle of F using the transformations tau(F) = (-a, b, -c), xi(F) = (c, b, a), chi(F) = (-c, b, -a), psi(F) = (-a, -b, -c), and the right neighbor R-i(F) of F for i >= 0.