## Communications in Mathematical Analysis

- Commun. Math. Anal.
- Volume 13, Number 2 (2012), 116-130.

### Meromorphic Functions Compatible with Homomorphisms of Actions on $\bf C$

R. N. Maalouf and W. Raji

#### Abstract

We consider homomorphisms $H:G_1\longrightarrow G_2$ of holomorphic (group or pseudo-group) actions $G_1$ and $G_2$ on domains $\Omega_1$ and $\Omega_2$ respectively in $\bf C$, together with meromorphic functions $f$ that are compatible with these homomorphisms in the sense that \begin{equation} f(g(z))=H(g)(f(z))\nonumber \end{equation} for every $g\in G_1$ and $z\in\Omega_1$. Such situations are rooted in the cases of elliptic and modular functions, modular and automorphic forms, etc... We investigate various aspects of such cases, such as constructions and correspondences between families of functions compatible with different homomorphisms, that transform one family of functions compatible with one homomorphism to another one compatible with a different homomorphism.

#### Article information

**Source**

Commun. Math. Anal., Volume 13, Number 2 (2012), 116-130.

**Dates**

First available in Project Euclid: 9 October 2012

**Permanent link to this document**

https://projecteuclid.org/euclid.cma/1349803598

**Mathematical Reviews number (MathSciNet)**

MR2998359

**Zentralblatt MATH identifier**

1348.30014

**Subjects**

Primary: 11F11: Holomorphic modular forms of integral weight

Secondary: 30D30: Meromorphic functions, general theory

**Keywords**

Meromorphic Functions Group Actions on {\bf C} Compatibility with Group Actions on {\bf C} Modular Forms Multiplier Systems

#### Citation

Maalouf, R. N.; Raji, W. Meromorphic Functions Compatible with Homomorphisms of Actions on $\bf C$. Commun. Math. Anal. 13 (2012), no. 2, 116--130. https://projecteuclid.org/euclid.cma/1349803598