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

Year 2007, Volume: 36 Issue: 2, 101 - 114, 01.02.2007

A. Tekcan

Abstract

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 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 τ (F) = (−a, b, −c), ξ(F) = (c, b, a),
χ(F) = (−c, b, −a), ψ(F) = (−a, −b, −c), and the right neighbor R
i
(F)
of F for i ≥ 0.

Keywords

Quadratic form, Indefinite form, Cycle, Proper cycle, Right neighbor, Base point

References

• Buchmann. J. Algorithms for Binary Quadratic Forms (Darmstadt, 2000).
• Flath, D. E. Introduction To Number Theory (Wiley, 1989).
• Tekcan, A. Proper cycles of indefinite quadratic forms and their right neighbors, Applications of Mathematics 52 (5), 407–415, 2007.