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

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

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 
@article{10_1007_s10492_007_0023_4,
     author = {Tekcan, Ahmet},
     title = {Proper cycles of indefinite quadratic forms and their right neighbors},
     journal = {Applications of Mathematics},
     pages = {407--415},
     publisher = {mathdoc},
     volume = {52},
     number = {5},
     year = {2007},
     doi = {10.1007/s10492-007-0023-4},
     mrnumber = {2342597},
     zbl = {1216.11042},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1007/s10492-007-0023-4/}
}
TY  - JOUR
AU  - Tekcan, Ahmet
TI  - Proper cycles of indefinite quadratic forms and their right neighbors
JO  - Applications of Mathematics
PY  - 2007
SP  - 407
EP  - 415
VL  - 52
IS  - 5
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.1007/s10492-007-0023-4/
DO  - 10.1007/s10492-007-0023-4
LA  - en
ID  - 10_1007_s10492_007_0023_4
ER  - 
%0 Journal Article
%A Tekcan, Ahmet
%T Proper cycles of indefinite quadratic forms and their right neighbors
%J Applications of Mathematics
%D 2007
%P 407-415
%V 52
%N 5
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.1007/s10492-007-0023-4/
%R 10.1007/s10492-007-0023-4
%G en
%F 10_1007_s10492_007_0023_4
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

Cité par Sources :