论文标题
$ e $ functions的微分方程和代数值的最小化
Minimization of differential equations and algebraic values of $E$-functions
论文作者
论文摘要
作为具有适当初始条件的线性微分方程的解决方案的解决方案，最小化的功率序列包括找到具有该功率序列作为解决方案的最小值的非平凡线性微分方程。这个问题都存在于同质和不均匀的变体中。它与差异操作员分解的经典问题不同，但与之相关。最近，最小化发现了超验数理论的应用，更具体地说，在计算非零代数点的计算中，siegel的$ e $ functions采用代数值。我们为这些问题提供了算法和实现，并讨论了示例和实验。
A power series being given as the solution of a linear differential equation with appropriate initial conditions, minimization consists in finding a non-trivial linear differential equation of minimal order having this power series as a solution. This problem exists in both homogeneous and inhomogeneous variants; it is distinct from, but related to, the classical problem of factorization of differential operators. Recently, minimization has found applications in Transcendental Number Theory, more specifically in the computation of non-zero algebraic points where Siegel's $E$-functions take algebraic values. We present algorithms and implementations for these questions, and discuss examples and experiments.
