Communications in Mathematical Analysis

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

R. N. Maalouf and W. Raji

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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

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

First available in Project Euclid: 9 October 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 11F11: Holomorphic modular forms of integral weight
Secondary: 30D30: Meromorphic functions, general theory

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


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

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