Bounding the degree of Belyi polynomials
作者: Jose Rodriguez
作者单位: 1Department of Mathematics, University of Berkeley, 743 Evans Hall, Berkeley, CA, United States
刊名: Journal of Number Theory, 2013, Vol.133 (9), pp.2892-2900
来源数据库: Elsevier Journal
DOI: 10.1016/j.jnt.2012.12.019
关键词: BelyiDessin dʼenfantNewton polygonP -AdicsHeight functionsHeightsBelyi heightBelyi functions
原始语种摘要: Abstract(#br)Text(#br)Belyiʼs theorem states that a Riemann surface X , as an algebraic curve, is defined over Q ¯ if and only if there exists a holomorphic function B taking X to P 1 C with at most three critical values { 0 , 1 , ∞ } . By restricting to the case where X = P 1 C and our holomorphic functions are Belyi polynomials, for an algebraic number λ , we define a Belyi height H ( λ ) to be the minimal degree of the set of Belyi polynomials with B ( λ ) ∈ { 0 , 1 } . We prove for non-zero λ with non-zero p -adic valuation, the Belyi height of λ is greater than or equal to p using the combinatorics of Newton polygons. We also give examples of algebraic numbers with relatively low height and show that our bounds are sharp.(#br)Video(#br)For a video summary of this paper,...
全文获取路径: Elsevier  (合作)
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影响因子:0.466 (2012)

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关键词翻译
关键词翻译
  • algebraic 代数的
  • height 高度
  • polygon 多边形
  • degree 
  • bounds 界限
  • minimal 最小的
  • combinatorics 组合数学
  • Dessin 敌螨通
  • mover 移动钮
  • video 影象