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Results tagged with cv.complex-variables
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user 38805
Complex analysis, holomorphic functions, automorphic group actions and forms, pseudoconvexity, complex geometry, analytic spaces, analytic sheaves.
12
votes
2
answers
971
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Is Every Holomorphic Near an Entire?
Let $K\subset \mathbb C$ be a closed subset of the complex plane, not necessarily bounded. Let $U$ be the interior of $K$.
Let $f:K\to \mathbb C$ be a continuous bounded function, whose restriction t …
- 1,113
2
votes
0
answers
158
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$\frac{1}{2}<\sigma<1$, is $f(n) = \Bigl| \,1+ \frac{1}{2^{\sigma + i n}} + \cdots + \frac{1...
We have $\frac{1}{2} < \sigma < 1$ and
$$
f(n) = \Bigl|\, 1+ \frac{1}{2^{\sigma + i n}} + \cdots + \frac{1}{n^{\sigma + i n}} \Bigr|
$$
. My goal is proving this statement that $|f(n)|$ is $O(\log n)$ …
- 1,113