Question

Show that a holomorph function $f:\mathbb{C}^{\times}\rightarrow\mathbb{C} $ doesn't exist which satisfies $f(z)^n=z$ for $n\in\mathbb{N}, n\gt1$.

score 123 · Answer 1 · 2018-05-05 10:37:13

Show that a holomorph function $f:\mathbb{C}^{\times}\rightarrow\mathbb{C} $ doesn't exist which satisfies $f(z)^n=z$ for $n\in\mathbb{N}, n\gt1$.

score 205 · Answer 2 · 2026-04-05 05:12:53

205

Views

Domain discretization

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score 48 · Answer 3 · 2026-04-13 11:06:43

48

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score 326 · Answer 4 · 2018-05-05 15:06:15

326

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score 206 · Answer 5 · 2026-04-11 21:52:57

206

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Clarify definition of $\left\lVert f \right\rVert _{\infty}$in Rudin's "Real & Complex Analysis"

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score 109 · Answer 7 · 2026-04-12 07:19:56

109

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score 253 · Answer 8 · 2018-05-06 06:30:59

253

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Show that $\sum\limits_{1\leq m^2+n^2 \leq R^2} \frac{1}{m^2+n^2} = 2\pi \log R +O(1)$ as $R\to \infty$

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67

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score 4.5k · Answer 11 · 2026-04-13 20:39:38

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score 522 · Answer 12 · 2026-04-12 17:06:38

522

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score 101 · Answer 13 · 2026-04-13 06:14:02

101

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if $0$ is not an accumulation point for $\{1/b_n\}$, then $\{b_n\}$ converges to $b$.

Published on 13 Apr 2026 - 6:14

score 84 · Answer 14 · 2026-04-12 01:06:09

84

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score 85 · Answer 15 · 2026-03-27 14:30:12

85

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List Question

Show that a holomorph function $f:\mathbb{C}^{\times}\rightarrow\mathbb{C} $ doesn't exist which satisfies $f(z)^n=z$ for $n\in\mathbb{N}, n\gt1$.

Domain discretization

Given average of positive bounded sequence converges to zero, does the average of the square sequence also converge?

$S^1-\{p\}$ is homeomorphic to $\mathbb{R}$

Clarify definition of $\left\lVert f \right\rVert _{\infty}$in Rudin's "Real & Complex Analysis"

Sheaf Theory for Complex Analysis

Make sense of taking 'differential' on both sides of a matrix equation

Show that $\sum\limits_{1\leq m^2+n^2 \leq R^2} \frac{1}{m^2+n^2} = 2\pi \log R +O(1)$ as $R\to \infty$

An estimating problem of integral

Convergence in probability of this sum

Differentiable at a point with positive derivative implies increasing in neighborhood of point?

Limit of divided differences.

if $0$ is not an accumulation point for $\{1/b_n\}$, then $\{b_n\}$ converges to $b$.

Fourier series and continuity

Proving the Completeness of a Metric Space

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