Tohoku Mathematical Journal, Second Series
Online ISSN : 2186-585X
Print ISSN : 0040-8735
ISSN-L : 0040-8735
SYMMETRY IN THE FUNCTIONAL EQUATION OF A LOCAL ZETA DISTRIBUTION
ANTHONY KABLE
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2006 Volume 58 Issue 4 Pages 493-507

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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.
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© 2006 by THE TOHOKU UNIVERSITY
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