Proper cycles of indefinite quadratic forms and their right neighbors

Ahmet Tekcan

Applications of Mathematics (2007)

  • Volume: 52, Issue: 5, page 407-415
  • ISSN: 0862-7940

Abstract

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In this paper we consider proper cycles of indefinite integral quadratic forms F = ( a , b , c ) with discriminant Δ . We prove that the proper cycles of F can be obtained using their consecutive right neighbors R i ( F ) for i ≥ 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 τ ( F ) = ( - a , b , - c ) and χ ( F ) = ( - c , b , - a ) .

How to cite

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Tekcan, Ahmet. "Proper cycles of indefinite quadratic forms and their right neighbors." Applications of Mathematics 52.5 (2007): 407-415. <http://eudml.org/doc/33298>.

@article{Tekcan2007,
abstract = {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 $\chi (F)=(-c,b,-a)$.},
author = {Tekcan, Ahmet},
journal = {Applications of Mathematics},
keywords = {quadratic form; indefinite form; cycle; proper cycle; right neighbor; indefinite binary quadratic form; cycle; proper cycle; right neighbor},
language = {eng},
number = {5},
pages = {407-415},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Proper cycles of indefinite quadratic forms and their right neighbors},
url = {http://eudml.org/doc/33298},
volume = {52},
year = {2007},
}

TY - JOUR
AU - Tekcan, Ahmet
TI - Proper cycles of indefinite quadratic forms and their right neighbors
JO - Applications of Mathematics
PY - 2007
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 52
IS - 5
SP - 407
EP - 415
AB - 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 $\chi (F)=(-c,b,-a)$.
LA - eng
KW - quadratic form; indefinite form; cycle; proper cycle; right neighbor; indefinite binary quadratic form; cycle; proper cycle; right neighbor
UR - http://eudml.org/doc/33298
ER -

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