Positive binary forms representing the same integers in an arithmetic progression
Acta Arithmetica, Tome 181 (2017) no. 2, pp. 111-126
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
In 1938, Delone proved that $(x^2+3y^2,x^2+xy+y^2)$ is the unique pair of non-equivalent positive definite primitive integral binary forms representing the same integers. We provide effective criteria on finding all pairs of positive definite integral binary forms representing the same integers in the set $A_{p,k}$ for any prime $p$ and any non-negative integer $k$ less than $p$, where $A_{p,k}$ is the set containing an arithmetic progression with common difference $p$ and initial term $k$.
Keywords:
delone proved unique pair non equivalent positive definite primitive integral binary forms representing integers provide effective criteria finding pairs positive definite integral binary forms representing integers set prime non negative integer where set containing arithmetic progression common difference initial term nbsp
Affiliations des auteurs :
Myung-Hwan Kim 1 ; Byeong-Kweon Oh 2
@article{10_4064_aa8443_6_2017,
author = {Myung-Hwan Kim and Byeong-Kweon Oh},
title = {Positive binary forms representing the same integers in an arithmetic progression},
journal = {Acta Arithmetica},
pages = {111--126},
publisher = {mathdoc},
volume = {181},
number = {2},
year = {2017},
doi = {10.4064/aa8443-6-2017},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/aa8443-6-2017/}
}
TY - JOUR AU - Myung-Hwan Kim AU - Byeong-Kweon Oh TI - Positive binary forms representing the same integers in an arithmetic progression JO - Acta Arithmetica PY - 2017 SP - 111 EP - 126 VL - 181 IS - 2 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.4064/aa8443-6-2017/ DO - 10.4064/aa8443-6-2017 LA - en ID - 10_4064_aa8443_6_2017 ER -
%0 Journal Article %A Myung-Hwan Kim %A Byeong-Kweon Oh %T Positive binary forms representing the same integers in an arithmetic progression %J Acta Arithmetica %D 2017 %P 111-126 %V 181 %N 2 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.4064/aa8443-6-2017/ %R 10.4064/aa8443-6-2017 %G en %F 10_4064_aa8443_6_2017
Myung-Hwan Kim; Byeong-Kweon Oh. Positive binary forms representing the same integers in an arithmetic progression. Acta Arithmetica, Tome 181 (2017) no. 2, pp. 111-126. doi: 10.4064/aa8443-6-2017
Cité par Sources :