| 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 |
| . |
