  In previous work, Ohno conjectured, and Nakagawa proved, relations between
the counting functions of certain cubic fields. These relations may be viewed
as complements to the Scholz reflection principle, and Ohno and Nakagawa
deduced them as consequences of `extra functional equations' involving the
Shintani zeta functions associated to the prehomogeneous vector space of binary
cubic forms.
  In the present paper we generalize their result by proving a similar identity
relating certain degree l fields with Galois groups D_l and F_l respectively,
for any odd prime l, and in particular we give another proof of the
Ohno-Nakagawa relation without appealing to binary cubic forms.
