On $\hat Z $-zeta function

International audienceWe present in this note a definition of zeta function of the field $\Qbb$ which incorporates all $p$-adic L-functions of Kubota-Leopoldt for all $p$ and also so called Soul\'e classes of the field $\Qbb$. This zeta function is a measure, which we construct using the action of the absolute Galois group $G_\Qbb$ on fundamental groups.}\abstract{We present in this note a definition of zeta function of the field $\Qbb$ which incorporates all $p$-adic L-functions of Kubota-Leopoldt for all $p$ and also so called Soul\'e classes of the field $\Qbb$. This zeta function is a measure, which we construct using the action of the absolute Galois group $G_\Qbb$ on fundamental groups