Title: Sigma function associated with a hyperelliptic curve with two points at infinity Show Chinese title

Title: 与无穷远点为两个的双曲面曲线相关的Sigma函数

Abstract: Baker constructed basic meromorphic functions on the Jacobian variety of a hyperelliptic curve with two points at infinity. We call them Baker functions. The construction is based on the Abel-Jacobi map, which allows us to identify the field of meromorphic functions on the Jacobian variety of the curve with the field of meromorphic functions on the symmetric product of the curve. In our previous paper, a solution to the KP equation was constructed in terms of the Baker function. This paper is devoted to the properties of the Baker functions. In this paper, we construct an entire function whose second logarithmic derivatives are the Baker functions. We prove that the power series expansion of the entire function around the origin is determined only by the coefficients of the defining equation of the curve and a branch point of the curve algebraically. We also describe the quasi-periodicity of the entire function and express the entire function in terms of the Riemann theta function. Show Chinese abstract

Abstract: 贝克在双曲线上无限点的雅可比流形上构造了基本的亚纯函数。 我们称它们为贝克函数。 该构造基于阿贝尔-雅可比映射，它允许我们将曲线的雅可比流形上的亚纯函数域与曲线的对称积上的亚纯函数域进行识别。 在我们之前的论文中，用贝克函数构造了KP方程的解。 本文专门研究贝克函数的性质。 在本文中，我们构造了一个整函数，其二阶对数导数是贝克函数。 我们证明了该整函数在原点处的幂级数展开仅由曲线定义方程的系数和曲线的一个代数分支点的系数决定。 我们还描述了该整函数的准周期性，并用黎曼θ函数表达了该整函数。