Definition 6

— Let K be a locally compact field$^{(1)}$. For $a \in K^*$, one calls modulus of a, and denotes by $\mathrm{mod}_K(a)$ or simply $\mathrm{mod}(a)$, the modulus of the automorphism $x \mapsto ax$ of the additive group $K^+$ underlying K; one sets $\mathrm{mod}(0) = 0$.