AI 中文总结
本文证明存在二元整函数定义的隐式芽，其解析延拓沿每条射线均失败，且模趋于无穷，从而否定地回答了 Eremenko 关于隐函数 Gross 性质的问题。
AI 中文摘要
1918 年，Gross 证明了平面上亚纯函数的正则局部逆可以沿从圆心出发的每条射线进行解析延拓，除非该方向属于勒贝格测度为零的集合。Eremenko 提出了一个问题：对于由两个变量的整关系定义的隐函数，同样的结论是否成立。我们证明了存在一个二元整函数 $F$ 和一个正则隐式芽 $\varphi$，由 $F(z,\varphi(z))=0$ 定义，其解析延拓在从圆心出发的每条射线上都失败。事实上，沿每条射线，延拓的模在接近奇点时趋于无穷大。
英文摘要
In 1918, Gross proved that a regular local inverse of a meromorphic function in the plane can be continued analytically along every ray from its centre except for directions in a set of Lebesgue measure zero. Eremenko asked whether the same conclusion holds for an implicit function defined by an entire relation in two variables. We prove that there exist an entire function $F$ of two variables and a regular implicit germ $φ$, defined by $F(z,φ(z))=0$, whose analytic continuation fails on every ray from its centre. In fact, along each ray, the modulus of the continuation tends to infinity as the singular point is approached.
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