Benford's law for linear recurrence sequences (Q1097907)

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.