论文标题
周期性的标准和椭圆功能的应用
Criteria for periodicity and an application to elliptic functions
论文作者
论文摘要
Let P and Q be relatively prime integers greater than 1, and f a real valued discretely supported function on a finite dimensional real vector space V. We prove that if f_{P}(x)=f(Px)-f(x) and f_{Q}(x)=f(Qx)-f(x) are both Λ-periodic for some lattice Λ\subset V, then so is f (up to a修改为0）。该结果用于证明椭圆函数场算术的定理。在最后一部分中，我们讨论了该定理的较高等级类似物，并解释了为什么在等级2中失败。关于较高等级案例的完整讨论将出现在即将到来的工作中。
Let P and Q be relatively prime integers greater than 1, and f a real valued discretely supported function on a finite dimensional real vector space V. We prove that if f_{P}(x)=f(Px)-f(x) and f_{Q}(x)=f(Qx)-f(x) are both Λ-periodic for some lattice Λ\subset V, then so is f (up to a modification at 0). This result is used to prove a theorem on the arithmetic of elliptic function fields. In the last section we discuss the higher rank analogue of this theorem and explain why it fails in rank 2. A full discussion of the higher rank case will appear in a forthcoming work.
