Geodesic
Proper cycles of indefinite quadratic forms and their right neighbors
Applications of Mathematics, Tome 52 (2007) no. 5, pp. 407-415.

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In this paper we consider proper cycles of indefinite integral quadratic forms $F=(a,b,c)$ with discriminant $\Delta $. We prove that the proper cycles of $F$ can be obtained using their consecutive right neighbors $R^i(F)$ for $i\ge 0$. 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 $\tau (F)=(-a,b,-c)$ and $\chi (F)=(-c,b,-a)$.
DOI : 10.1007/s10492-007-0023-4
Classification : 11E04, 11E12, 11E16
Keywords: quadratic form; indefinite form; cycle; proper cycle; right neighbor 
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Tekcan, Ahmet. Proper cycles of indefinite quadratic forms and their right neighbors. Applications of Mathematics, Tome 52 (2007) no. 5, pp. 407-415. doi : 10.1007/s10492-007-0023-4. http://geodesic.mathdoc.fr/articles/10.1007/s10492-007-0023-4/

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