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On the cycles of indefinite quadratic forms and cycles of ideals II

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2010-01-01

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Southeast Asian Mathematical Soc-seams

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Abstract

Let P and Q be two positive integers such that P < Q and let D = P-2 + Q(2) be a positive non- square integer. In the first section, we give some preliminaries from binary quadratic forms and quadratic ideals. In the second section, we show that given an ideal I = [Q, P + root D], there exists an indefinite symmetric quadratic form F-I = (Q, 2P,-Q) of discriminant 4 D which corresponds to I. We prove that I is always reduced, and so is F-I. Further, we prove that the cycle of F-I can be obtained using the cycle of I.

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Quadratic forms, Cycles of forms, Ideals, Cycles of ideals, Science & technology, Physical sciences, Mathematics

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