## Benford’s law for linear recurrence sequences.(English)Zbl 0636.10007

In section 2 the authors prove: Theorem 2.1. Let $$\{y_ n\}_{n=1,2,...}$$ be an integer sequence generated by the recursion formula $$y_{n+1}=ry_ n+f(n)$$, $$n=1,2,..$$. If the series $$\sum^{\infty}_{n=1}f(n)/r^{n-1}$$ is convergent, then the sequence $$\{y_ n\}_{n=1,2,...}$$ obeys Benford’s law except for the case $$r=10^ m$$ with m being some nonnegativenumber of primitive representations of a positive definite quadratic form by a given even unimodular positive definite quadratic form. Finally the well-known estimate $$a_ f(T)=O((\det T)^{k/2})$$ for a cusp form f is improved.
Reviewer: A.Krieg

### MSC:

 11B37 Recurrences 11K16 Normal numbers, radix expansions, Pisot numbers, Salem numbers, good lattice points, etc.
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