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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:
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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