AI 中文总结
本文证明了二维Jacobian猜想整数系数反例的渐近值路径仅含有限个整数格点，并应用Theta函数理论于实数域和复数域上的该猜想。
AI 中文摘要
我们证明了任何具有整数系数且其Jacobian矩阵行列式等于一的二维Jacobian猜想的反例，其渐近值路径只能包含平面整数格中的有限多个点。我们论文的第二部分给出了某些Theta函数理论在实数域和复数域上的二维Jacobian猜想中的一些非平凡应用。
英文摘要
We prove that any counter-example to the two dimensional Jacobian Conjecture with integral coefficients and determinant of its Jacobian matrix equals one, has only paths of asymptotic values that can contain only finitely many points of the planar integral lattice. The second part of our paper gives some nontrivial applications of the theory of certain Theta functions to the two dimensional Jacobian Conjecture over the real field, and over the complex field.
