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On standard L-functions attached to automorphic forms on definite orthogonal groups
Published online by Cambridge University Press: 22 January 2016
Abstract.
We show an explicit functional equation of the standard L-function associated with an automorphic form on a definite orthogonal group over a totally real algebraic number field. This is a completion and a generalization of our previous paper, in which we constructed standard L-functions by using Rankin-Selberg convolution and the theory of Shintani functions under certain technical conditions. In this article we remove these conditions. Furthermore we show that the L-function of f has a pole at s = m/2 if and only if f is a constant function.
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- Copyright © Editorial Board of Nagoya Mathematical Journal 1998
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