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

Abstract

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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.

How to cite

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Taniguchi, 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 -

References

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