 Self-dual Haar measure

Relative to a nontrivial additive character, the self-dual additive Haar measure makes the twice-applied Fourier transform over a local field equal to reflection. If the annihilator of the valuation ring is ${\pi }^c{\mathcal{O}}_F$ and its residue field has $q$ elements, the normalization is $\mathrm{vol}({\mathcal{O}}_F)=q^{c/2}$. Volumes of a compact open subgroup and its character annihilator then multiply to one.