Question

Show $\not\exists$ $f\in O(\mathbb{C})$ holomorphic such that $f(z)=\overline{z}$ when $|z|=1$.

score 342 · Answer 1 · 2026-04-09 02:02:07

342

Views

Show $\not\exists$ $f\in O(\mathbb{C})$ holomorphic such that $f(z)=\overline{z}$ when $|z|=1$.

Published on 09 Apr 2026 - 2:02

score 163 · Answer 2 · 2026-04-09 02:09:51

163

Views

Show $f(w)=\frac{1}{2\pi i}\int_{\partial \Omega} f(z)\frac{g'(z)}{g(z)-g(w)}\,dz$ for $w\in\Omega$

Published on 09 Apr 2026 - 2:09

score 37 · Answer 3 · 2026-04-08 22:52:33

37

Views

$B=\{t\in[-T,T]:|f(\sigma+it)|>\ell\}$, does it hold that $|B|>\epsilon 2T$

Published on 08 Apr 2026 - 22:52

score 55 · Answer 4 · 2026-03-25 22:04:51

55

Views

Complex analysis: prove that $ |\int_{\gamma} f(z) dz| \leq M \ell (\gamma) $

Published on 25 Mar 2026 - 22:04

score 3.4k · Answer 5 · 2026-04-09 16:35:26

3.4k

Views

Real-valued functions on complex numbers

Published on 09 Apr 2026 - 16:35

score 150 · Answer 6 · 2026-04-10 16:25:53

150

Views

Finding branch cut and choice of logarithm

Published on 10 Apr 2026 - 16:25

score 316 · Answer 7 · 2026-04-08 22:55:44

316

Views

Show that $|f(0)| \leq \frac{1}{4}$ for every holomorphic function $f:\Bbb D \to \Bbb D$ such that $|f(\frac{1}{2})|+|f(-\frac{1}{2})|=0$

Published on 08 Apr 2026 - 22:55

score 5.7k · Answer 8 · 2026-04-11 13:33:39

5.7k

Views

Solving $\sin(z)=0$ for complex numbers $z$ by using Euler's formula

Published on 11 Apr 2026 - 13:33

score 391 · Answer 9 · 2026-04-09 06:58:51

391

Views

The reciprocal transformation

Published on 09 Apr 2026 - 6:58

score 123 · Answer 10 · 2018-02-02 11:01:12

Let $f$ be an entire function, if $100 \log(\mid z \mid) \geq \mid f(z) \mid$ for $\mid z \mid \geq 2$, then is $f$ constant?

score 230 · Answer 11 · 2026-04-11 12:58:33

230

Views

Simple question about Taylor expansion of Dirichlet's eta function validity

Published on 11 Apr 2026 - 12:58

score 87 · Answer 12 · 2026-04-08 16:40:14

87

Views

Help with basic inequality (complex numbers)

Published on 08 Apr 2026 - 16:40

score 240 · Answer 13 · 2026-04-06 22:57:40

240

Views

Little help with a residue integration with branch point

Published on 06 Apr 2026 - 22:57

score 52 · Answer 14 · 2026-04-09 00:54:33

52

Views

Period of f given

Published on 09 Apr 2026 - 0:54

score 59 · Answer 15 · 2026-04-09 03:39:08

59

Views

help with the proof - regular points of a union of sets

Published on 09 Apr 2026 - 3:39

List Question

Show $\not\exists$ $f\in O(\mathbb{C})$ holomorphic such that $f(z)=\overline{z}$ when $|z|=1$.

Show $f(w)=\frac{1}{2\pi i}\int_{\partial \Omega} f(z)\frac{g'(z)}{g(z)-g(w)}\,dz$ for $w\in\Omega$

$B=\{t\in[-T,T]:|f(\sigma+it)|>\ell\}$, does it hold that $|B|>\epsilon 2T$

Complex analysis: prove that $ |\int_{\gamma} f(z) dz| \leq M \ell (\gamma) $

Real-valued functions on complex numbers

Finding branch cut and choice of logarithm

Show that $|f(0)| \leq \frac{1}{4}$ for every holomorphic function $f:\Bbb D \to \Bbb D$ such that $|f(\frac{1}{2})|+|f(-\frac{1}{2})|=0$

Solving $\sin(z)=0$ for complex numbers $z$ by using Euler's formula

The reciprocal transformation

Let $f$ be an entire function, if $100 \log(\mid z \mid) \geq \mid f(z) \mid$ for $\mid z \mid \geq 2$, then is $f$ constant?

Simple question about Taylor expansion of Dirichlet's eta function validity

Help with basic inequality (complex numbers)

Little help with a residue integration with branch point

Period of f given

help with the proof - regular points of a union of sets

Trending Questions

Popular # Hahtags

Popular Questions