标题： 全景残差和椭圆可求和性 显示英文标题

标题： Panorbital residues and elliptic summability

摘要： 对于椭圆曲线中的非扭点定义的翻译自同构$\tau$，我们考虑决定给定的椭圆函数$f$是否为某个椭圆函数$g$的形式$f=\tau(g)-g$的椭圆可求和问题。我们引入了两个新的全轨道残差，并证明它们与Dreyfus、Hardouin、Roques和Singer在2018年引入的轨道残差一起，构成了椭圆可求和问题的完整障碍。底层的椭圆曲线可以用任何通常的方式描述：作为一个复数环面，作为一个Tate曲线，或者作为一个一维阿贝尔簇。我们在每种情况下从头开始内在地发展必要的结果；在最后两种情况下，我们还在任意特征下进行工作。我们包括了一些基本的具体例子，在每种情况下计算了一些可求和和不可求和函数的轨道和全轨道残差。最后，我们应用轨道和全轨道残差的技术来获得几个独立感兴趣的新的结果。 显示英文摘要

摘要： For $\tau$ the translation automorphism defined by a non-torsion point in an elliptic curve, we consider the elliptic summability problem of deciding whether a given elliptic function $f$ is of the form $f=\tau(g)-g$ for some elliptic function $g$. We introduce two new panorbital residues and show that they, together with the orbital residues introduced in 2018 by Dreyfus, Hardouin, Roques, and Singer, comprise a complete obstruction to the elliptic summability problem. The underlying elliptic curve can be described in any of the usual ways: as a complex torus, as a Tate curve, or as a one-dimensional abelian variety. We develop the necessary results from scratch intrinsically within each setting; in the last two of them, we also work in arbitrary characteristic. We include several basic concrete examples of computation of orbital and panorbital residues for some summable and non-summable functions in each setting. We conclude by applying the technology of orbital and panorbital residues to obtain several new results of independent interest.