Published March 27, 2011
| Version 2855
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Neighbors of Indefinite Binary Quadratic Forms
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In this paper, we derive some algebraic identities on
right and left neighbors R(F) and L(F) of an indefinite binary
quadratic form F = F(x, y) = ax2 + bxy + cy2 of discriminant
Δ = b2 -4ac. We prove that the proper cycle of F can be given by
using its consecutive left neighbors. Also we construct a connection
between right and left neighbors of F.
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References
- J.Buchmann and U.Vollmer. Binary Quadratic Forms: An Algorithmic Approach. Springer-Verlag, Berlin, Heidelberg, 2007.
- D.A.Buell. Binary Quadratic Forms, Clasical Theory and Modern Computations. Springer-Verlag, New York, 1989.
- D.E.Flath. Introduction to Number Theory. Wiley, 1989.
- R.A. Mollin. Advanced Number Theory with Applications. CRC Press, Taylor and Francis Group, Boca Raton, London, New York, 2009.
- A.Tekcan and O.Bizim. The Connection between Quadratic Forms and the Extended Modular Group. Mathematica Bohemica 128(3)(2003), 225- 236.
- A.Tekcan. Proper Cycle of Indefinite Quadratic Forms and their Right Neighbors. Applications of Mathematics 52(5)(2007), 407-415.
- A.Tekcan. A Second Approach to the Proper Cycles of Indefinite Quadratic Forms and their Right Neighbors. Int. Journal of Contemporary Math. Sci. 2(6)(2007), 249-260.