On arithmetic progressions on Edwards curves

• Autorzy: Enrique González-Jiménez
• Języki publikacji: EN

Abstrakty

EN

Let $m ∈ ℤ_{>0}$ and a,q ∈ ℚ. Denote by $𝓐𝓟_{m}(a,q)$ 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 $𝓐𝓟_{m}(a,q)$ and we parametrize it by the rational points of an algebraic curve.

Kategorie tematyczne

• 11G30: Curves of arbitrary genus or genus ≠ 1 over global fields
• 14G05: Rational points
• 11D45: Counting solutions of Diophantine equations
• 11G05: Elliptic curves over global fields
• 11B25: Arithmetic progressions

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 2015
• Tom: 167
• Numer: 2
• Strony: 117-132

Daty

wydano

2015

Twórcy

autor

Enrique González-Jiménez

• Departamento de Matemáticas, Universidad Autónoma de Madrid
• Instituto de Ciencias Matemáticas (ICMat), Madrid, Spain

Identyfikatory

DOI

10.4064/aa167-2-2