On the arithmetic of the hyperelliptic curve y 2 = x n + a

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• 作者：Kevser Aktaş ; Hasan Şenay
• 关键词：hyperelliptic curve ; Lang’s conjecture
• 刊名：Czechoslovak Mathematical Journal
• 出版年：2016
• 出版时间：March 2016
• 年：2016
• 卷：66
• 期：1
• 页码：35-40
• 全文大小：108 KB
• 参考文献：[1] C. Birkenhake, H. Lange: Complex Abelian Varieties. Grundlehren der Mathematischen Wissenschaften 302, Springer, Berlin, 2004.MATH
  [2] S. Lang: Hyperbolic and Diophantine analysis. Bull. Am. Math. Soc., New Ser. 14 (1986), 159–205.MathSciNet CrossRef MATH
  [3] J. Wolfart: The’ Obvious’ part of Belyi’s theorem and Riemann surfaces with many automorphisms. Geometric Galois Actions. 1. Around Grothendieck’s “Esquisse d’un Programme” (L. Schneps et al., eds.). Proc. Conf. on geometry and arithmetic of moduli spaces, Luminy, France, 1995. Lond. Math. Soc. Lect. Note Ser. 242, Cambridge University Press, Cambridge, 1997, pp. 97–112.
  [4] J. Wolfart: Taylorentwicklungen automorpher Formen und ein Transzendenzproblem aus der Uniformisierungstheorie. Abh. Math. Semin. Univ. Hamb. 54 (1984), 25–33. (In German.)MathSciNet CrossRef MATH
  [5] J. Wolfart, G. Wüstholz: Der Überlagerungsradius gewisser algebraischer Kurven und die Werte der Betafunktion an rationalen Stellen. Math. Ann. 273 (1985), 1–15. (In German.)MathSciNet CrossRef MATH
  
• 作者单位：Kevser Aktaş (1)
  Hasan Şenay (2)
  
  1. Department of Mathematics, Faculty of Science, Selçuk University, Campus, 42003, Selçuklu, Konya, Turkey
  2. Department of Mathematics Education, Mevlana University, Yeni Istanbul Cad 235, 42003, Selçuklu, Konya, Turkey
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  Analysis
  Convex and Discrete Geometry
  Ordinary Differential Equations
  Mathematical Modeling and IndustrialMathematics
  
• 出版者：Springer Netherlands
• ISSN：1572-9141

文摘

We study the arithmetic properties of hyperelliptic curves given by the affine equation y 2 = x n +a by exploiting the structure of the automorphism groups. We show that these curves satisfy Lang’s conjecture about the covering radius (for some special covering maps).