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Results tagged with cv.complex-variables
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user 18850
Complex analysis, holomorphic functions, automorphic group actions and forms, pseudoconvexity, complex geometry, analytic spaces, analytic sheaves.
1
vote
what a Complex powers of operators to be the identity?
Here is a very dumb answer. Let your operator to be
$$
\Delta=(i-1)I, \Delta(f)=if-f
$$
Then it is trivial to verify that
$$
(1+\Delta)^{4}f=f, 4>0
$$
So for the problem to be interesting, some extra …
- 6,249
0
votes
intersection of holomorphic curve with hyperplane
I think the general answer would be unbounded unless you restrict $f$ to be some special class of entire functions. But the reason for this is trivial; namely you can approximate any continuous comple …
- 6,249
2
votes
Rouché's Theorem in complex analysis on the relation of the number of zeros and poles of mer...
Dear Mr. Cunningham:
The question you son asked is at an elementary level, but it has a wide range of associations. I think a one good reference is Prof. Tao's article:
https://terrytao.wordpress.com/ …
- 6,249
6
votes
Theta functions on an elliptic curve and Serre duality
Here is a 'low-brow' approach. One type of the result you are talking about has been written up implicitly in Lang's book Introduction to Arakelov theory. The case for cohomology of the elliptic curv …
- 6,249