On the Quadratic Irrationals, Quadratic Ideals and Indefinite Quadratic Forms
Ahmet Tekcan, Hacer Özden · Irish Mathematical Society Bulletin · 2006
Let P and Q be two rational integers, D = 1 be a positive non-square integer, and let δ = √ D or 1+ √ D 2 be a real quadratic irrational with trace t = δ+δ and norm n = δδ.Given any quadratic irrational γ = P +δ Q , there exist a quadratic ideal Iγ = [Q, δ + P ] and an indefinite quadratic formIn this paper, we obtain some properties of quadratic irrationals γ, quadratic ideals Iγ and indefinite quadratic forms Fγ .