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Proper cycles of indefinite quadratic forms and their right neighbors

Ahmet Tekcan (2007)

Applications of Mathematics

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 χ ( F ) = ( - c , b , - a ) .

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