Self-dual Haar measure (source code)

= Self-dual Haar measure
{title2=$\operatorname{vol}(\mathcal O_F)=q^{c/2}$}

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 $\operatorname{vol}(\mathcal O_F)=q^{c/2}$. Volumes of a compact open subgroup and its <character annihilator> then multiply to one.