## Nagoya Mathematical Journal

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

Takahiko Ueno

#### Abstract

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.

#### Article information

Source
Nagoya Math. J., Volume 175 (2004), 1-37.

Dates
First available in Project Euclid: 27 April 2005

https://projecteuclid.org/euclid.nmj/1114632092

Mathematical Reviews number (MathSciNet)
MR2085308

Zentralblatt MATH identifier
1075.11042

#### Citation

Ueno, Takahiko. Modular forms arising from zeta functions in two variables attached to prehomogeneous vector spaces related to quadratic forms. Nagoya Math. J. 175 (2004), 1--37. https://projecteuclid.org/euclid.nmj/1114632092

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