Proper cycles of indefinite quadratic forms and their right neighbors |
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Authors: | Ahmet Tekcan |
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Institution: | 1.Faculty of Science, Department of Mathematics,Uludag University,Bursa,Turkey |
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Abstract: | In this paper we consider proper cycles of indefinite integral quadratic forms F = (a, b, c) with discriminant Δ. We prove that the proper cycles of F can be obtained using their consecutive right neighbors R
i(F) for i ⩾ 0. We also derive explicit relations in the cycle and proper cycle of F when the length l of the cycle of F is odd, using the transformations τ(F) = (−a, b, −c) and ϰ(F) = (−c, b, −a). |
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Keywords: | quadratic form indefinite form cycle proper cycle right neighbor |
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