The introduction of Fourier analysis in number theory dates
back to Tate's thesis and at the time greatly clarified the
functional equation of L-series. For global function fields,
the local characters seem to be given by a residue. Lifting
to characteristic zero, we will see that this is indeed the
case. Back to number theory, we will give some speculations
how the characters, as originally defined by Tate in an ad
hoc manner, could be viewed as residues as well.