Communications in Mathematical Analysis

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

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 $$f(g(z))=H(g)(f(z))\nonumber$$ 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

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

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