The zeta function of a formal language L is the series exp(

${\sum}_{n\ge 1}{a}_{n}{x}^{n}/n)$, where

${a}_{n}$ 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

${\sum}_{n\ge 0}{a}_{n}{x}^{n}$ of L (which is rational, L being regular). He shows, under the same hypothesis, that there are cyclic languages

${L}_{1}$ and

${L}_{2}$ such that the generating function G(L) of L is

$G\left({L}_{1}\right)-G\left({L}_{2}\right)$ (a language is cyclic if (i) uv

$\in L\iff vu\in L$ and (ii)

$w\in L\iff {w}^{n}\in L$ (n

$\ge 1\left)\right)$. Moreover, it is decidable whether the zeta function of a regular language is rational.