## Journal of Mathematics of Kyoto University

### Differential equations for Hilbert modular forms of $\mathbb{Q}(\sqrt{2})$

Toshiyuki Mano

#### Abstract

We construct a system of non-linear differential equations from the uniformizing differential equations of an orbifold attached to certain Hilbert modular surface. Generic solutions of this system can be given by the logarithmic derivatives of Hilbert modular forms.

#### Article information

Source
J. Math. Kyoto Univ., Volume 44, Number 3 (2004), 457-477.

Dates
First available in Project Euclid: 14 August 2009

https://projecteuclid.org/euclid.kjm/1250283078

Digital Object Identifier
doi:10.1215/kjm/1250283078

Mathematical Reviews number (MathSciNet)
MR2103777

Zentralblatt MATH identifier
1087.11027

#### Citation

Mano, Toshiyuki. Differential equations for Hilbert modular forms of $\mathbb{Q}(\sqrt{2})$. J. Math. Kyoto Univ. 44 (2004), no. 3, 457--477. doi:10.1215/kjm/1250283078. https://projecteuclid.org/euclid.kjm/1250283078