## Missouri Journal of Mathematical Sciences

### A Transformation Law of an Eta Product and the Invariance of a Class of Entire Modular Functions Under $\Gamma _0 (n)$

#### Abstract

We present a new proof, using Residue Calculus, of the transformation law of a general eta product under $\Gamma_0(n)$ where $n$ is any integer, then we deduce the invariance of a special case of this product under this group and we prove the transformation law of another special case. Our proof is inspired by Siegel's proof [7] of the transformation law of the Dedekind eta function and by Rademacher's generalization [5].

#### Article information

Source
Missouri J. Math. Sci., Volume 20, Issue 2 (2008), 102-114.

Dates
First available in Project Euclid: 14 September 2011

Raji, Wissam; Gimenez, Jose. A Transformation Law of an Eta Product and the Invariance of a Class of Entire Modular Functions Under $\Gamma _0 (n)$. Missouri J. Math. Sci. 20 (2008), no. 2, 102--114. https://projecteuclid.org/euclid.mjms/1316032811