The volumes of Miyauchi subgroups

Abstract

Miyauchi described the $L$ and $\epsilon$-factors attached to generic representations of the unramified unitary group of rank three in terms of local newforms defined by a sequence of subgroups. We calculate the volumes of these Miyauchi groups.

The paper has been revised as follows in v3: Our results have now been generalized to include even residue characteristic. We added some remarks on ramification in a new section 1.4. There was an error in Lemma 9 in earlier versions of this paper, which has now been corrected in v3. This is the final version of the paper, which is to appear in Archiv der Mathematik