证明D-Finite类数学猜想的新方法

A New Method to Prove Mathematical Conjecture of D-Finite Class

摘要: 提出并证明了基于Morley三分线定理的Morley三角形微分定理(Gauss曲率指针细数定理)。根据该定理三点共线的结论构建了直角三角形及其镜像与Möbius函数对应的关联模型，为进一步研究Möbius函数的插值算法和离散性质奠定了基础；该定理还揭示了泛函的本质是泛函“一维”，并为进一步将泛函一维的几何性质推广到泛函“平面”指出了研究方向；论文中的定理、推论和开放性问题揭示了一次多项式向量场的极限环性质和二次多项式向量场的研究途径。给出了证明非交换D-finite类猜想的新方法。

Abstract: This paper presents and proves the Morley differential theorem (Gauss curvature pointer fineness theorem) based on Morley’s theorem. According to the conclusion of the three-point collinearity of this theorem, a correlation model between the right triangle and its mirror image and the Möbius function is constructed, which lays a foundation for the further study of the interpolation algorithm and discrete properties of the Möbius function. This theorem reveals that the nature of functional is functional “one-dimensional”, which lays a foundation for further extending the geometric properties of functional one-dimensional to functional “plane”. The theorems, corollaries and open problems in this paper reveal the properties of limit cycles of vector fields of first order polynomials and the research approaches of vector fields of quadratic polynomials. The new method to prove non-commutative D-finite class conjectures is given.