In this paper, we consider the most non-split parabolic D_4 type
prehomogeneous vector space. The vector space is an analogue of the space of
Hermitian forms. We determine the principal part of the zeta function

Yukie, Akihiko

English

arXiv

. In this paper, we consider the most non-split parabolic D 4 type prehomogeneous vector space. The vector space is an analogue of the space of Hermitian forms. We determine the principal part of the zeta function. Introduction  Throughout this paper, k is a number field. Let k 1 be a cubic extension of k,  and k 2 the Galois closure of k 1 . Then either k 2 = k 1 is a cyclic cubic extension of k or k 2 is an S 3 --extension of k. In this paper, we consider the zeta function defined for a prehomogeneous vector space (G; V ) which becomes the D 4 case in [6] after extending the base field from k to k 2 . We consider the most non-split case here and the vector space is an analogue of the space of Hermitian forms except it depends on three two dimensional vectors. So we call this space the space of binary tri-Hermitian forms. We discussed the meaning of this case in [1]. The purpose of this paper is to determine the principal part of the zeta function. Our main result is Theorem (3.6). In..

Akihiko Yukie

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On The Shintani Zeta Function For The Space Of Binary Tri-Hermitian Forms

http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.51.1336

On the Shintani zeta function for the space of binary tri-Hermitian forms

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