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Modular forms arising from zeta functions in two variables attached to prehomogeneous vector spaces related to quadratic forms

Published online by Cambridge University Press:  22 January 2016

Takahiko Ueno
Takahiko Ueno*
Affiliation:
Department of Mathematics, Rikkyo University, Nishi-Ikebukuro, Tokyo, 171-8501, Japan, ueno@rkmath.rikkyo.ac.jp
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Abstract

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In this paper, we prove the functional equations for the zeta functions in two variables associated with prehomogeneous vector spaces acted on by maximal parabolic subgroups of orthogonal groups. Moreover, applying the converse theorem of Weil type, we show that elliptic modular forms of integral or half integral weight can be obtained from the zeta functions.

Keywords

11F66
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 175 , 2004 , pp. 1 - 37
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2004

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