On arithmetic progressions on Edwards curves

Enrique González-Jiménez. "On arithmetic progressions on Edwards curves." Acta Arithmetica 167.2 (2015): 117-132. <http://eudml.org/doc/279397>.

@article{EnriqueGonzález2015,
abstract = {Let $m ∈ ℤ_\{>0\}$ and a,q ∈ ℚ. Denote by $_\{m\}(a,q)$ the set of rational numbers d such that a, a + q, ..., a + (m-1)q form an arithmetic progression in the Edwards curve $E_d : x² + y² = 1 + dx²y²$. We study the set $_\{m\}(a,q)$ and we parametrize it by the rational points of an algebraic curve.},
author = {Enrique González-Jiménez},
journal = {Acta Arithmetica},
keywords = {arithmetic progression; Edward curves; elliptic curved},
language = {eng},
number = {2},
pages = {117-132},
title = {On arithmetic progressions on Edwards curves},
url = {http://eudml.org/doc/279397},
volume = {167},
year = {2015},
}

TY - JOUR
AU - Enrique González-Jiménez
TI - On arithmetic progressions on Edwards curves
JO - Acta Arithmetica
PY - 2015
VL - 167
IS - 2
SP - 117
EP - 132
AB - Let $m ∈ ℤ_{>0}$ and a,q ∈ ℚ. Denote by $_{m}(a,q)$ the set of rational numbers d such that a, a + q, ..., a + (m-1)q form an arithmetic progression in the Edwards curve $E_d : x² + y² = 1 + dx²y²$. We study the set $_{m}(a,q)$ and we parametrize it by the rational points of an algebraic curve.
LA - eng
KW - arithmetic progression; Edward curves; elliptic curved
UR - http://eudml.org/doc/279397
ER -