# On the zeta functions of prehomogeneous vector spaces for a pair of simple algebras

Takashi Taniguchi^{[1]}

- [1] University of Tokyo Graduate School of Mathematical Sciences 3–8–1 Komaba Megoro-Ku Tokyo 153-0041 (Japan)

Annales de l’institut Fourier (2007)

- Volume: 57, Issue: 4, page 1331-1358
- ISSN: 0373-0956

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topTaniguchi, Takashi. "On the zeta functions of prehomogeneous vector spaces for a pair of simple algebras." Annales de l’institut Fourier 57.4 (2007): 1331-1358. <http://eudml.org/doc/10260>.

@article{Taniguchi2007,

abstract = {In this paper we consider the prehomogeneous vector space for a pair of simple algebras which are inner forms of the $D_4$ type and the $E_6$ type. We mainly study the non-split cases. The main purpose of this paper is to determine the principal parts of the global zeta functions associated with these spaces when the simple algebras are non-split. We also give a description of the sets of rational orbits of these spaces, which clarifies the expected density theorems arising from the properties of these zeta functions.},

affiliation = {University of Tokyo Graduate School of Mathematical Sciences 3–8–1 Komaba Megoro-Ku Tokyo 153-0041 (Japan)},

author = {Taniguchi, Takashi},

journal = {Annales de l’institut Fourier},

keywords = {prehomogeneous vector space; zeta function; simple algebra; global zeta function; Shintani zeta-function},

language = {eng},

number = {4},

pages = {1331-1358},

publisher = {Association des Annales de l’institut Fourier},

title = {On the zeta functions of prehomogeneous vector spaces for a pair of simple algebras},

url = {http://eudml.org/doc/10260},

volume = {57},

year = {2007},

}

TY - JOUR

AU - Taniguchi, Takashi

TI - On the zeta functions of prehomogeneous vector spaces for a pair of simple algebras

JO - Annales de l’institut Fourier

PY - 2007

PB - Association des Annales de l’institut Fourier

VL - 57

IS - 4

SP - 1331

EP - 1358

AB - In this paper we consider the prehomogeneous vector space for a pair of simple algebras which are inner forms of the $D_4$ type and the $E_6$ type. We mainly study the non-split cases. The main purpose of this paper is to determine the principal parts of the global zeta functions associated with these spaces when the simple algebras are non-split. We also give a description of the sets of rational orbits of these spaces, which clarifies the expected density theorems arising from the properties of these zeta functions.

LA - eng

KW - prehomogeneous vector space; zeta function; simple algebra; global zeta function; Shintani zeta-function

UR - http://eudml.org/doc/10260

ER -

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