Commenced in January 2007
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Neighbors of Indefinite Binary Quadratic Forms

Authors: Ahmet Tekcan


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.

Keywords: cycle, Quadratic form, indefinite form, proper cycle, right neighbor, left neighbor

Digital Object Identifier (DOI):

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