Summary: Automatic Dirichlet series
J.­P. Allouche
CNRS, LRI
B“atiment 490
F­91405 Orsay Cedex (France)
allouche@lri.fr
M. Mend`es France
Universit'e Bordeaux I
Math'ematiques
F­33405 Talence Cedex (France)
mmf@math.u­bordeaux.fr
J. Peyri`ere
Universit'e Paris­Sud
Math'ematiques, B“atiment 425
F­91405 Orsay Cedex (France)
jacques.peyriere@math.u­psud.fr
Abstract
Dirichlet series whose coefficients are generated by finite automata define meromor­
phic functions on the whole complex plane. As consequences, a new proof of Cobham's
theorem on the existence of logarithmic frequencies of symbols in automatic sequences

Source: Allouche, Jean-Paul - Laboratoire de Recherche en Informatique, Université de Paris-Sud 11

Collections: Computer Technologies and Information Sciences