论文标题
Weierstrass Zeta功能的准期
The quasi-periods of the Weierstrass zeta-function
论文作者
论文摘要
我们研究WeierStrass $ζ$ function的比率$ p =η_1/η_2$，依赖于比率$τ=ω_1/ω_2$的基础秩-2晶格的发电机的比率。我们将提供地图$τ\ mapsto p（τ）$的明确几何描述。结果，我们获得了Heins对定理的解释，该定理表明$ p $在Riemann Sphere中获得了无限的经常值。我们的主要结果是在古典文献中隐含的，但似乎并不是很众所周知。 本质上，这是一张说明性论文。我们希望它很容易访问，并可以作为这些古典主题的介绍。
We study the ratio $p=η_1/η_2$ of the pseudo-periods of the Weierstrass $ζ$-function in dependence of the ratio $τ=ω_1/ω_2$ of the generators of the underlying rank-2 lattice. We will give an explicit geometric description of the map $τ\mapsto p(τ)$. As a consequence, we obtain an explanation of a theorem by Heins who showed that $p$ attains every value in the Riemann sphere infinitely often. Our main result is implicit in the classical literature, but it seems not to be very well known. Essentially, this is an expository paper. We hope that it is easily accessible and may serve as an introduction to these classical themes.
