Question

Exercise on zeros of an entire function

score 588 · Answer 1 · 2019-12-09 20:16:45

588

Views

Exercise on zeros of an entire function

Published on 09 Dec 2019 - 20:16

score 82 · Answer 2 · 2019-12-13 10:48:24

82

Views

Image of $|z|>1$ is a dense set

Published on 13 Dec 2019 - 10:48

score 217 · Answer 3 · 2019-12-13 16:41:24

217

Views

For an entire function $f(z)$, is it true that $f(z)=f(\bar{z})$ for all complex $z$?

Published on 13 Dec 2019 - 16:41

score 110 · Answer 4 · 2026-02-25 11:16:05

110

Views

How to prove a complex function is constant if it is given that complex function is entire function (Holomorphic function).

Published on 25 Feb 2026 - 11:16

score 577 · Answer 5 · 2019-12-15 22:18:09

577

Views

An example of an entire function, which is not polynomial, that has only one zero.

Published on 15 Dec 2019 - 22:18

score 90 · Answer 6 · 2019-12-29 23:47:21

90

Views

If $f : \mathbb{C} \rightarrow \mathbb{C}$ is an entire function such that $|f(z)| \leq 1 + \sqrt{|z|}$, then $f$ is a constant function

Published on 29 Dec 2019 - 23:47

score 181 · Answer 7 · 2020-01-02 01:33:50

181

Views

An entire function with a bound on its integral is constant

Published on 02 Jan 2020 - 1:33

score 74 · Answer 8 · 2026-03-22 23:26:06

74

Views

$f$ is entire without any zeros, then for $ r>0$ $m(r) = \inf\left \{ \left|f(z)\right |:\left|z\right|=r\right \}$, $m$ is non increasing

Published on 22 Mar 2026 - 23:26

score 2.4k · Answer 9 · 2020-01-17 05:33:17

2.4k

Views

show that an entire function with the nth derivative zero is polynomial of degree at most n-1

Published on 17 Jan 2020 - 5:33

score 78 · Answer 10 · 2020-01-18 14:15:58

78

Views

Entire function bounded by a polynomial is a polynomial with a less or equal degree- complex function

Published on 18 Jan 2020 - 14:15

score 112 · Answer 11 · 2020-01-21 06:53:01

112

Views

Show that either $f\left(c\right)=0$ or $f$ is constant in $D$.

Published on 21 Jan 2020 - 6:53

score 333 · Answer 12 · 2020-01-27 11:27:56

333

Views

Show that there is no entire function such that $f(\frac 1n)=\frac{n}{3n-2},\forall n\in\mathbb{N}$

Published on 27 Jan 2020 - 11:27

score 74 · Answer 13 · 2020-01-27 12:05:14

74

Views

Consider an entire function $f$. What can be said about $\inf_{z\in\mathbb{C}}|f(z)|$?

Published on 27 Jan 2020 - 12:05

score 361 · Answer 14 · 2020-01-28 15:36:25

361

Views

Proving entire function is identically zero

Published on 28 Jan 2020 - 15:36

score 59 · Answer 15 · 2020-01-28 19:02:35

59

Views

If $|f(z)|\le |g(z^2)|$ for all $ z\in\mathbb{C} $, then $ f(z) =f(-z), \forall z\in\mathbb{C} $

Published on 28 Jan 2020 - 19:02

List Question

Exercise on zeros of an entire function

Image of $|z|>1$ is a dense set

For an entire function $f(z)$, is it true that $f(z)=f(\bar{z})$ for all complex $z$?

How to prove a complex function is constant if it is given that complex function is entire function (Holomorphic function).

An example of an entire function, which is not polynomial, that has only one zero.

If $f : \mathbb{C} \rightarrow \mathbb{C}$ is an entire function such that $|f(z)| \leq 1 + \sqrt{|z|}$, then $f$ is a constant function

An entire function with a bound on its integral is constant

$f$ is entire without any zeros, then for $ r>0$ $m(r) = \inf\left \{ \left|f(z)\right |:\left|z\right|=r\right \}$, $m$ is non increasing

show that an entire function with the nth derivative zero is polynomial of degree at most n-1

Entire function bounded by a polynomial is a polynomial with a less or equal degree- complex function

Show that either $f\left(c\right)=0$ or $f$ is constant in $D$.

Show that there is no entire function such that $f(\frac 1n)=\frac{n}{3n-2},\forall n\in\mathbb{N}$

Consider an entire function $f$. What can be said about $\inf_{z\in\mathbb{C}}|f(z)|$?

Proving entire function is identically zero

If $|f(z)|\le |g(z^2)|$ for all $ z\in\mathbb{C} $, then $ f(z) =f(-z), \forall z\in\mathbb{C} $

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