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

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

Let F = (a, b, c) be an indefinite quadratic form of discriminant ∆ > 0.In the first section, we give some preliminaries from binary quadraticforms. In the second section, we derive some results concerning thebase points of indefinite quadratic forms in the cycle and proper cycleof 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 Ri(F)of F for i ≥ 0.
Keywords:

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

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  • 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.
Hacettepe Journal of Mathematics and Statistics-Cover
  • Yayın Aralığı: 6
  • Başlangıç: 2002
  • Yayıncı: Hacettepe Üniversitesi Fen Fakultesi
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THE BASE POINTS OF INDEFINITE QUADRATIC FORMS IN THE CYCLE AND PROPER CYCLE OF AN INDEFINITE QUADRATIC FORM

Ahmet TEKCAN