Question

Is the Principal Logarithm Function Entire and Can Its Value Ever Be Less Than 0?

score 43 · Answer 1 · 2019-05-13 02:23:04

43

Views

Is the Principal Logarithm Function Entire and Can Its Value Ever Be Less Than 0?

Published on 13 May 2019 - 2:23

score 71 · Answer 2 · 2019-05-13 11:43:50

71

Views

Local behavior of range of complex polynomial

Published on 13 May 2019 - 11:43

score 305 · Answer 3 · 2019-05-14 22:15:30

305

Views

A power series with real coefficients which evaluates to $0$ for every positive real number

Published on 14 May 2019 - 22:15

score 42 · Answer 4 · 2019-05-18 18:03:11

42

Views

Does there exist an entire function with $f(0)=1$ and $f(4i)=i$ and $|f(z_1) - f(z_2)| < |z_1 - z_2|^{\frac{\pi}{3}}$ in $1<|z|<3$?

Published on 18 May 2019 - 18:03

score 528 · Answer 5 · 2019-05-19 00:39:14

528

Views

$f$ entire and $Im(f(z)) \leq Re(f(z))^2$ implies $f$ is constant

Published on 19 May 2019 - 0:39

score 146 · Answer 6 · 2019-05-20 19:42:50

146

Views

Using Cauchy's Estimate for Lower Bound of Entire Function

Published on 20 May 2019 - 19:42

score 1.2k · Answer 7 · 2019-05-22 10:14:32

1.2k

Views

Entire function of finite order with infinitely many zeros

Published on 22 May 2019 - 10:14

score 384 · Answer 8 · 2019-05-24 21:44:42

384

Views

Finding an entire function such that $|f(z)| \leq |\exp(z)|$ and $f(\pi i)$

Published on 24 May 2019 - 21:44

score 96 · Answer 9 · 2019-05-25 10:20:57

96

Views

Values of $p$ such that $f(z)$ is an entire function

Published on 25 May 2019 - 10:20

score 1.7k · Answer 10 · 2019-05-30 08:50:10

1.7k

Views

$f(ax)=f(x)^2-1$, what is $f$?

Published on 30 May 2019 - 8:50

score 85 · Answer 11 · 2019-05-30 23:57:44

85

Views

To show $f$ is constant.

Published on 30 May 2019 - 23:57

score 271 · Answer 12 · 2026-03-25 04:38:11

271

Views

Entire function non identically zero implies that limit sequence of zeros diverges

Published on 25 Mar 2026 - 4:38

score 50 · Answer 13 · 2019-06-04 09:41:30

50

Views

Existence of entire function (Rosay-Rudin's paper)

Published on 04 Jun 2019 - 9:41

score 935 · Answer 14 · 2019-06-04 22:50:22

935

Views

If $f$ is an entire function and $f(z) \not \in [0,1]$ for every $z$, then $f$ is constant

Published on 04 Jun 2019 - 22:50

score 993 · Answer 15 · 2019-06-10 07:53:22

993

Views

An entire function $f$ such that $g(z)=\overline{f(\bar{z})}$

Published on 10 Jun 2019 - 7:53

List Question

Is the Principal Logarithm Function Entire and Can Its Value Ever Be Less Than 0?

Local behavior of range of complex polynomial

A power series with real coefficients which evaluates to $0$ for every positive real number

Does there exist an entire function with $f(0)=1$ and $f(4i)=i$ and $|f(z_1) - f(z_2)| < |z_1 - z_2|^{\frac{\pi}{3}}$ in $1<|z|<3$?

$f$ entire and $Im(f(z)) \leq Re(f(z))^2$ implies $f$ is constant

Using Cauchy's Estimate for Lower Bound of Entire Function

Entire function of finite order with infinitely many zeros

Finding an entire function such that $|f(z)| \leq |\exp(z)|$ and $f(\pi i)$

Values of $p$ such that $f(z)$ is an entire function

$f(ax)=f(x)^2-1$, what is $f$?

To show $f$ is constant.

Entire function non identically zero implies that limit sequence of zeros diverges

Existence of entire function (Rosay-Rudin's paper)

If $f$ is an entire function and $f(z) \not \in [0,1]$ for every $z$, then $f$ is constant

An entire function $f$ such that $g(z)=\overline{f(\bar{z})}$

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