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Proceedings of the National Academy of Sciences of the United States of America logoLink to Proceedings of the National Academy of Sciences of the United States of America
. 1972 May;69(5):1081–1082. doi: 10.1073/pnas.69.5.1081

On Zeta Functions Associated with Prehomogeneous Vector Spaces

Mikio Sato 1,2,3, Takuro Shintani 1,2,3
PMCID: PMC426633  PMID: 16591979

Abstract

In this note, we construct certain families of Dirichlet series that satisfy functional equations. We shall also indicate an arithmetical application of our results. The work presented here depends upon the theory of prehomogeneous vector spaces.

Keywords: algebraic groups, gamma function, Dirichlet series

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