Question

If $g: \mathbb{C} \rightarrow \mathbb{C} $ with $\Delta(g)=\Delta(f)=2 \pi u$ and $\lim_{z \rightarrow \infty} f(z)-g(z)=0.$ Then $g=f.$

score 43 · Answer 1 · 2016-03-15 15:01:38

If $g: \mathbb{C} \rightarrow \mathbb{C} $ with $\Delta(g)=\Delta(f)=2 \pi u$ and $\lim_{z \rightarrow \infty} f(z)-g(z)=0.$ Then $g=f.$

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List Question

If $g: \mathbb{C} \rightarrow \mathbb{C} $ with $\Delta(g)=\Delta(f)=2 \pi u$ and $\lim_{z \rightarrow \infty} f(z)-g(z)=0.$ Then $g=f.$

Branch points of $f : \mathbb{C} \to \mathbb{P}^1 : z \mapsto \frac{1}{2}(z + \frac{1}{z})$

Deck transformation of $p : Y \to X : z \mapsto z^3 - 3z$

Riemann surface for square root function

Riemann surface of $f(z)=((z-1)(z-2)(z-3))^{2/3}$

Linear fractional transformation of quadratic differentials on the Riemann sphere

Euler characteristic singular surface

Maximal analytic continuation gives rise to a covering

Pullback of a complex $ 1$-form

How to prove the number of poles minus the number of zeros is $2-2g$?

For $h$ an odd degree polynomial, $\{(z,w)\in\mathbb{C}^2\mid w^2=h(z)\}$ can be made into a compact Riemann surface by adding 1 point at inifinty

Constant Curvature Metric and Biholomorphic Equivalence

Upper half-plane $\overline{\mathbb{H}}$ with two boundary punctures

Counting zeroes of global sections

Equation of a Riemann surface?

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