论文标题
Quaternionic椭圆功能的周期关系
Period Relations for Quaternionic Elliptic Functions
论文作者
论文摘要
我们研究了Quaternionic分析中的椭圆功能，并证明了复杂情况的一些经典定理的类似物。主要的结果是在H/L上的闭合差分1形式的周期与3型的时期之间的关系，其中L是H中的晶格。通过在Quaternionic分析的意义上施加适用的形式，我们获得了Riemann时期的Quaternionic类似物的Abelian表面。我们还获得了Legendre关系的Quaternionic类似物，作为$2π^2 $的平等和四个Quasi-weierstrass $ζ$ function的四个准词的线性组合，其中该系数是L.左侧的左右阶层的合理函数。准期。
We study elliptic functions in quaternionic analysis, and prove some analogues of classical theorems from the complex case. The main result is a relation between the periods of closed differential 1-forms and 3-forms on H/L where L is a lattice in H. By applying to forms that are regular in the sense of quaternionic analysis, we obtain quaternionic analogues of Riemann's period relations for an abelian surface. We also obtain a quaternionic analogue of Legendre's relation, as an equality between $2π^2$ and a linear combination of the four quasi-periods of the quaternionic Weierstrass $ζ$-function, where the coefficients are rational functions of a basis for L. When L is a left-ideal for a maximal order in a definite quaternion algebra over Q, we obtain three further relations among the quasi-periods.
