Tohoku Mathematical Journal
2006
December
SECOND SERIES VOL. 58, NO. 4

Tohoku Math. J.
58 (2006), 493-507

Title SYMMETRY IN THE FUNCTIONAL EQUATION OF A LOCAL ZETA DISTRIBUTION

Author Anthony Kable

(Received March 16, 2005, revised October 5, 2005)
Abstract. We examine the structure of the coefficient matrix in the functional equation of the zeta distribution of a self-adjoint prehomogeneous vector space over a non-Archimedean local field. Under a restrictive assumption on the generic stabilizers, we show that this matrix is block upper-triangular with almost symmetric blocks; this generalizes a result of Datskovsky and Wright for the space of binary cubic forms.

2000 Mathematics Subject Classification. Primary 11S90.
Key words and phrases. Prehomogeneous vector space, local functional equation.

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