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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

Atsushi Murase  and
Takashi Sugano
Atsushi Murase
Affiliation:
Department of Mathematics, Faculty of Science, Kyoto Sangyo University, Motoyama, Kamigamo Kita-ku, Kyoto 603-8555, Japan, murase@cc.kyoto-su.ac.jp
Takashi Sugano
Affiliation:
Department of Mathematics, Faculty of Science, Kanazawa University, Kakuma-machi, Kanazawa 920-1192, Japan, sugano@kappa.s.kanazawa-u.ac.jp
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Abstract.

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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.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 152 , December 1998 , pp. 57 - 96
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1998

References

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