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Results tagged with cv.complex-variables
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user 8435
Complex analysis, holomorphic functions, automorphic group actions and forms, pseudoconvexity, complex geometry, analytic spaces, analytic sheaves.
16
votes
1
answer
2k
views
What are some of the earliest examples of analytic continuation?
I'm wondering how Riemann knew that $\zeta(z)$ could be extended to a larger domain. In particular, who was the first person to explicitly extend the domain of a complex valued function and what was …
- 3,699
1
vote
2
answers
376
views
Global theory of holomorphic functions [closed]
I am trying to develop a theory explaining analytic continuation of a holomorphic function $f(z)$ defined on an open set $D \subset \mathbb{C}$. Recently, I was looking at the last chapter of Lars Ah …
- 3,699
18
votes
2
answers
5k
views
How did Riemann calculate the first few non-trivial zeros of the zeta-function?
Does anyone know how Riemann calculated the first few non-trivial zeros of the Zeta function? I am wondering if he approximated the integral, $\frac{1}{2 \pi i} \int_{R} \frac{{\xi}^\prime(z)}{\xi (z …
- 3,699
29
votes
1
answer
2k
views
Riemann's attempts to prove RH
I read somewhere that Riemann believed he could find a representation of the zeta function that would allow him to show that all the non-trivial zeros of the zeta function lie on the critical line. I …
- 3,699
35
votes
7
answers
6k
views
Heuristic argument for the Riemann Hypothesis
Is there a heuristic argument that supports the validity of the Riemann hypothesis or are we just relying on numerical evidence? Moreover, what is the strongest theorem that supports the validity of …
- 3,699