离散线性系中Benford定律的一个特征
A characterization of Benford's Law in discrete-time linear systems
摘要：
一个充要条件（“非共振”）建立的自治线性差分方程的每一个解决方案，或更一般地为每个序列$(x^\top A^n y)$与$x,y\in \mathbb{R}^d$和$A\in \mathbb{R}^{d\times d}$，是平凡的，否则符合本福德定律（对数分布的重要性）的强形式。该条件包含文献中所有相关结果作为特例。它的数论的影响进行了讨论的背景下，具体的例子，所以它可能的扩展和修改。
英文摘要：
A necessary and sufficient condition ("nonresonance") is established for every solution of an autonomous linear difference equation, or more generally for every sequence $(x^\top A^n y)$ with $x,y\in \mathbb{R}^d$ and $A\in \mathbb{R}^{d\times d}$, to be either trivial or else conform to a strong form of Benford's Law (logarithmic distribution of significands). This condition contains all pertinent results in the literature as special cases. Its number-theoretical implications are discussed in the context of specific examples, and so are its possible extensions and modifications.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
