Explicit solutions to the Oppenheim conjecture for indefinite ternary diagonal forms

Abstract

We prove the Oppenheim conjecture for indefinite ternary diagonal forms of the type $x^2+y^2-\alpha z^2$ where $\alpha$ is an irrational number. Our method is explicit in the sense that we are able to construct a solution to the problem and we obtain an effective bound on the solution. The method is geometrical and is based on continued fractions.

Some typos corrected