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

2004/03/16 by Takashi Taniguchi, Taniguchi, Takashi
Computer Science · Mathematics · #11M41 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Matrix Theory and Algorithms #Number Theory (math.NT) #Representation Theory (math.RT) #math.NT #math.RT #msc:11M41

paper · pdf · doi:10.48550/arxiv.math/0403253

20 pages, AMS LaTeX

arxiv created 2004/03/16 · openalex publication_date 2004/03/16 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we consider the prehomogeneous vector space for pair of simple algebras which are k-forms of the D₄ type and the E₆ 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 in the non-split cases. We also give a description of the sets of rational orbits of these spaces, which suggests the expected density theorems arising from the properties of these zeta functions.

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