Optimalité pour un problème de Bézivin
作者: David Adam
刊名: Journal de théorie des nombres de Bordeaux, 2019, Vol.31 (1), pp.161-177
来源数据库: The Center for Diffusion of Academic Mathematical Journals
DOI: 10.5802/jtnb.1073
关键词: Fonctions entières arithmétiques
原始语种摘要: Let $q$ be an integer such that $|q|\ge 2$ and $s$ be a positive integer. In this article, we show that an entire function $f$ such that $\varlimsup _{r\rightarrow +\infty }\frac{\ln |f|_r}{\ln ^3r}<\frac{4s}{27\ln ^2|q|}$ and taking Gaussian integer values on $\lbrace q^m+iq^n\mid m,n\in \mathbb{N}\rbrace $, as well as its $s-1$ first derivatives, is a polynomial. Moreover, the bound $\frac{4s}{27\ln ^2|q|}$ is optimal. This generalizes and improves a result obtained by Bézivin in [1].
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关键词翻译
关键词翻译
  • polynomial 多项式
  • optimal 最佳的
  • integer 整数
  • first 第一
  • entire 完整的
  • taking 摄影
  • function 函数
  • well 
  • values 价值观
  • derivatives 派生物