Questions tagged [meromorphic-functions]

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Transformation of Julia set sequence emerging from meromorphic function

I consider a sequence of meromorphic functions on the Riemann sphere $f_k:\hat{\mathbb{C}} \to \hat{\mathbb{C}}$ for $k\in\mathbb{N}$ of the form $$f_k(z)=\sum_{j=1}^{n_k}\dfrac{1}{(z-p_j)^{c_j}}$$ ...
Jens Fischer's user avatar
3 votes
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Topology of level sets for meromorphic function

Let $F$ be a meromorphic function on $\mathbb{C}$. I consider the "level set" $$E_\varepsilon=\{z:|F(z)|\leq\varepsilon\}.$$ My objective is to find conditions under which $E_\varepsilon$ ...
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Tilings of the plane and meromorphic functions on the plane

This question has three up-votes on m.s.e. but isn't getting any answers. Every textbook says every doubly-periodic meromorphic function on $\mathbb C$ has a fundamental domain that is a ...
Michael Hardy's user avatar
2 votes
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Triangulating Riemann surfaces by using non-constant meromorphic functions

Let $X$ be a connected Riemann surface, i.e. $X$ is a one dimensional connected complex manifold (Hausdorff and second-countable as a topological space). The following is a classical result: Theorem (...
John117's user avatar
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principal divisor on complex surfaces

Let $X$ be a non compact complex surface non projective and non algebraic, and let $S$ be compact Riemann surface embedded in $X$ ( i mean that $S$ is a compact complex sub variety of $X$ of ...
singularity's user avatar
1 vote
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418 views

Dimension of global holomorphic sections of a line bundle

Let $K$ be the canonical line bundle of a compact Riemann surface $M$ of genus $g$. Consider the pull back of $K$ on $M \times M$ via projection on the first factor. What is the dimension of the space ...
Roch's user avatar
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On a map between Riemann surfaces of genus $1$

Let $C$ be a compact Riemann surface of genus $1$, and $p\in C$, and $w$ be a local holomorphic coordinate on $C$ near $p$ with $w=0$ at $p$. As usual, for a divisor $D$ denote by $L(D)$ the vector ...
DesmondMiles13's user avatar
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Meromorphic extension of a limit function

Suppose $f_j(z)$, $j=1,2,..$ is a sequence of meromorphic functions on the complex plane $\mathbb{C}$. With a common set of all poles given by $S = \{-i,-2i, -3i,..\}$. Assume that each of them is ...
2inftyandBeyond's user avatar
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Does a vector over the field of meromorphic functions describe a manifold?

Assume that the variables $\mathbf x=(x_1,...,x_n)$ are coordinates on the solution manifold of a differential equation $\mathbf D(\mathbf x,\dot{\mathbf x},\ldots,\mathbf x^{(\alpha)})=\mathbf 0$ ...
emma's user avatar
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Coefficients of a special meromorphic function

The problem described below appears elementary, but I can't figure out the answer or find it in the literature. I apologize if I have missed something very basic. Let me begin with considering a ...
Dierk Bormann's user avatar