# A Characterization of Benford’s Law in Discrete-Time Linear Systems

@article{Berger2014ACO, title={A Characterization of Benford’s Law in Discrete-Time Linear Systems}, author={Arno Berger and Gideon Eshun}, journal={Journal of Dynamics and Differential Equations}, year={2014}, volume={28}, pages={431-469} }

- Published 2014
DOI:10.1007/s10884-014-9393-y

A necessary and sufficient condition (“nonresonance”) is established for every solution of an autonomous linear difference equation, or more generally for every sequence $$(x^\top A^n y)$$(x⊤Any) with $$x,y\in \mathbb {R}^d$$x,y∈Rd and $$A\in \mathbb {R}^{d\times d}$$A∈Rd×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… CONTINUE READING

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