THE RAMANUJAN JOURNAL, Vol. 10, No. 3 (2005), 341-382.

An Infinite Product Formula for the Elliptic Modular Function $\lambda(\tau)$

MASAAKI YOSHIDA
Department of Mathematics, Kyushu University, Fukuoka 810-8560, Japan
Email: myoshida@math.kyushu-u.ac.jp

Received November 20, 2002; Accepted February 14, 2005

Abstract. We present an infinite product for the elliptic modular form $\lambda(\tau)$ of the following form:
$$

\lambda(\tau)=\prod_{\gamma\in\Gamma}\frac{\tau - \gamma(0)}{\tau - \gamma(1)}, $$
where $\Gamma$ is an extension of the elliptic modular group $\Gamma(2)$ of index $2$.

Keywords: automorphic function, hypergeometric equation, infinite product, Lambda function, monodromy group, Schottky group

2000 Mathematics Classification: Primary 11F03, 30B99, 33B99, 33C05

MATHSCINET: 2193384

Original article available at www.springerlink.com:
http://springerlink.metapress.com/openurl.asp?genre=article&id=doi:10.1007/s11139-005-4854-x

Sat Jul 8 10:52:07 EDT 2006