TY - JFULL
AU - Ahmet Tekcan and Arzu Özkoç
PY - 2009/12/
TI - Quadratic Irrationals, Quadratic Ideals and Indefinite Quadratic Forms II
T2 - International Journal of Mathematical and Computational Sciences
SP - 1062
EP - 1066
VL - 3
SN - 1307-6892
UR - https://publications.waset.org/pdf/2294
PU - World Academy of Science, Engineering and Technology
NX - Open Science Index 35, 2009
N2 - Let 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. Let γ = P+δ Q be a quadratic irrational for positive integers P and Q. Given a quadratic irrational γ, there exist a quadratic ideal Iγ = [Q, δ + P] and an indeﬁnite quadratic form Fγ(x, y) = Q(x−γy)(x−γy) of discriminant Δ = t
2−4n. In the ﬁrst section, we give some preliminaries form binary quadratic forms, quadratic irrationals and quadratic ideals. In the second section, we obtain some results on γ, Iγ and Fγ for some speciﬁc values of Q and P.
ER -