The zeta function of a formal language L is the series exp(
is the number of words of length n in L. The author shows that if L is regular and if its zeta function is regular, then it has integer coefficients and each irreducible factor of its numerator and denominator divides the denominator of the generating function
of L (which is rational, L being regular). He shows, under the same hypothesis, that there are cyclic languages
such that the generating function G(L) of L is
(a language is cyclic if (i) uv
. Moreover, it is decidable whether the zeta function of a regular language is rational.