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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1answer
205 views
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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0answers
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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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79 views
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 ...
4
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1answer
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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1answer
231 views
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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0answers
104 views
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 ...
