# Article

 Title: Proper cycles of indefinite quadratic forms and their right neighbors (English) Author: Tekcan, Ahmet Language: English Journal: Applications of Mathematics ISSN: 0862-7940 (print) ISSN: 1572-9109 (online) Volume: 52 Issue: 5 Year: 2007 Pages: 407-415 Summary lang: English . Category: math . Summary: 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 $\chi (F)=(-c,b,-a)$. (English) Keyword: quadratic form Keyword: indefinite form Keyword: cycle Keyword: proper cycle Keyword: right neighbor MSC: 11E04 MSC: 11E12 MSC: 11E16 idZBL: Zbl 1216.11042 idMR: MR2342597 DOI: 10.1007/s10492-007-0023-4 . Date available: 2009-09-22T18:30:49Z Last updated: 2020-07-02 Stable URL: http://hdl.handle.net/10338.dmlcz/134685 . Reference: [1] J.  Buchmann: Algorithms for Binary Quadratic Forms.Springer-Verlag, accepted. Zbl 0948.11051 Reference: [2] D.  E.  Flath: Introduction to Number Theory.Wiley, New York, 1989. Zbl 0651.10001, MR 0972739 .

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