Mean asymptotic behaviour of radix-rational sequences and dilation equations.

The generating series of a radix-rational sequence is a rational formal power series from formal language theory viewed through a fixed radix numeration system. For each radix-rational sequence with complex values we prove the existence of an asymptotic expansion in the usual scale of the $N^\alpha\log^\beta(N)$'s, but with variable coefficients. The precision of the asymptotic expansion depends on the joint spectral radius of a finite family of matrices; the coefficients are obtained through some dilation equations.

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Virginie Collette
Last modified: Wed Aug 24 14:52:58 CEST 2011