# Questions tagged [meromorphic-functions]

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7
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### What is meromorphic differentials like on Riemann Sphere? [closed]

There is a proposition that every meromorphic differential on Riemann Sphere (or $\mathbb{P}^1 = \mathbb{C} \cup \{ \infty \}$) can be written as $f dz$ where $f$ is a meromorphic function on $\mathbb{...

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### Some simple algebra of rational functions by André Weil

In André Weil's dissertation, he considers two meromorphic functions $x,y$ on a complex curve. He assumes every pole of $y$ is a pole of $x$, and its multiplicity as a pole of $y$ is no greater than ...

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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 ...

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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 ...

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121 views

### Poles of an integral of a meromorphic function with toric poles

Suppose I have a meromorphic function in several variables $f(x_1,\ldots,x_k,y_1,\ldots,y_m)$ and I want to integrate along the torus $T^m$ given by $|y_1|=\cdots=|y_m|=1$. It is not true in general ...

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### A “prequestion” about meromorphic representations of algebraic groups

In a comment exchange around an answer to Is a group scheme determined by its category of representations? there arose the issue of Tannakian reconstruction for non-affine algebraic groups (e. g. ...

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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 ...