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Results tagged with cv.complex-variables
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user 17907
Complex analysis, holomorphic functions, automorphic group actions and forms, pseudoconvexity, complex geometry, analytic spaces, analytic sheaves.
7
votes
Elementary Proof of Riemann-Roch for Compact Riemann Surfaces
The proof given in Otto Forster, Lectures on Riemann Surfaces (Graduate Texts in Mathematics 81), chapter 16, seems very much suited to your list of prerequisites.
- 4,746
7
votes
Demystifying complex numbers
Another classic I haven't seen mentioned yet is the proof of the Machin formula
$$
\frac{\pi}{4} = 4\arctan \frac{1}{5}-\arctan \frac{1}{239}.
$$
I honestly don't know a proof of this that avoids comp …
12
votes
Demystifying complex numbers
This is a specific example where complex numbers aid a task in elementary real analysis; I haven't thought about the extent to which it generalizes.
In my first year, I was given the task of formally …