Geodesic
On arithmetic progressions on Edwards curves
Enrique González-Jiménez1
1 Departamento de Matemáticas Universidad Autónoma de Madrid and Instituto de Ciencias Matemáticas (ICMat) Madrid, Spain
Acta Arithmetica, Tome 167 (2015) no. 2, pp. 117-132.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

Let $m\in {\mathbb {Z}}_{>0}$ and $a,q\in {\mathbb {Q}}$. Denote by $\mathcal {AP}_{m}(a,q)$ the set of rational numbers $d$ such that $a,a+q,\dots ,a+(m-1)q$ form an arithmetic progression in the Edwards curve $E_d : x^2+y^2=1+dx^2 y^2$. We study the set $\mathcal {AP}_{m}(a,q)$ and we parametrize it by the rational points of an algebraic curve.
DOI : 10.4064/aa167-2-2
Keywords: mathbb mathbb denote mathcal set rational numbers dots m form arithmetic progression edwards curve study set mathcal parametrize rational points algebraic curve

Enrique González-Jiménez 1

1 Departamento de Matemáticas Universidad Autónoma de Madrid and Instituto de Ciencias Matemáticas (ICMat) Madrid, Spain 
@article{10_4064_aa167_2_2,
     author = {Enrique Gonz\'alez-Jim\'enez},
     title = {On arithmetic progressions on {Edwards} curves},
     journal = {Acta Arithmetica},
     pages = {117--132},
     publisher = {mathdoc},
     volume = {167},
     number = {2},
     year = {2015},
     doi = {10.4064/aa167-2-2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/aa167-2-2/}
}
TY  - JOUR
AU  - Enrique González-Jiménez
TI  - On arithmetic progressions on Edwards curves
JO  - Acta Arithmetica
PY  - 2015
SP  - 117
EP  - 132
VL  - 167
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4064/aa167-2-2/
DO  - 10.4064/aa167-2-2
LA  - en
ID  - 10_4064_aa167_2_2
ER  - 
%0 Journal Article
%A Enrique González-Jiménez
%T On arithmetic progressions on Edwards curves
%J Acta Arithmetica
%D 2015
%P 117-132
%V 167
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4064/aa167-2-2/
%R 10.4064/aa167-2-2
%G en
%F 10_4064_aa167_2_2
Enrique González-Jiménez. On arithmetic progressions on Edwards curves. Acta Arithmetica, Tome 167 (2015) no. 2, pp. 117-132. doi : 10.4064/aa167-2-2. http://geodesic.mathdoc.fr/articles/10.4064/aa167-2-2/

Cité par Sources :