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Dergiler / Turkish Journal of Mathematics / 2022 / Cilt: 46 - Sayı: 3

Composition laws on the Fricke surface and Markov triples

Esra Ünal YILMAZ
Abdurrahman Muhammed ULUDAĞ
Sayfa
785–799
Yayın Tarihi
2022-11-01
DOI
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

This latter surface admits the squares of Markov triples as its solutions.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:We determine some composition laws related to the Fricke surface and the “double” Fricke surface.
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Temel Bulgular & Veri:We determine some composition laws related to the Fricke surface and the “double” Fricke surface.
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Sonuç & Katkı:This latter surface admits the squares of Markov triples as its solutions.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Alan Parametreleri

Abstract

We determine some composition laws related to the Fricke surface and the “double” Fricke surface. This latter surface admits the squares of Markov triples as its solutions.

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Bu Makaleye Atıf Yap

YILMAZ, E. Ü., ULUDAĞ, A. M. (2022). Composition laws on the Fricke surface and Markov triples. Turkish Journal of Mathematics, Cilt: 46 - Sayı: 3, 785–799. https://ajindex.com/articles/607290

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Kaynakça (6)

  1. Aigner M. Markov’s Theorem and 100 Years of the Uniqueness Conjecture. Springer New York 2013
  2. Cohn H. Representation of Markoff’s binary quadratic forms by geodesics on a perforated torus. Acta Arithmetica 1971; 18; 125-136
  3. Lemmermeyer F. Conics-A Poor Man’s Elliptic Curves, arXiv:math/0311306, 2003
  4. Manin, Yu I. Cubic forms: algebra, geometry, arithmetic, Elsevier, 1986
  5. Perrine S. Sommes de Dedekind et generalisations de l’equation diophantienne de Markoff, Journal of Number Theory, 1994; 2: 224-247, 2002 (in French)
  6. Perrine S., Sur la conjecture de Frobenius relative aux solutions de l’équation de Markoff (Première partie), 2014 (in French).