Relations de récurrence linéaires, primitivité et loi de Benford

Details Relations de récurrence linéaires, primitivité et loi de Benford Relations de récurrence linéaires, primitivité et loi de Benford

2010-07-23

arxiv.org/abs/1007.5349v3

Mathematics

Dynamical Systems

12 pages; title updated, theorem 2 completed

Scientific paper

We prove that many sequences of positive numbers $(a_n)$ defined by finite
linear difference equations $a_{n+k}=c_{k-1}a_{n+k-1}+...+c_0a_n$ with suitable
non negative reals coefficients $c_i$ satisfy Bendford's Law on the first digit
in many bases $b>2$. Our techniques rely on Perron-Frobenius theory via the
companion matrix of the characteristic polynomial of the defining equation.

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