Question

order of zero of modular form from it's expansion at infinity

score 451 · Answer 1 · 2026-03-17 12:49:41

451

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order of zero of modular form from it's expansion at infinity

Published on 17 Mar 2026 - 12:49

score 46 · Answer 2 · 2026-03-22 06:47:28

46

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Holomorphic domain of $ \Phi\left(z\right)=\ln\left(\frac{z-a}{z+a}\right)$

Published on 22 Mar 2026 - 6:47

score 1.2k · Answer 3 · 2026-03-20 06:35:13

1.2k

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Complex Analysis - Harmonic function as real part of holomorphic function

Published on 20 Mar 2026 - 6:35

score 74 · Answer 4 · 2026-03-22 12:24:53

74

Views

Impossibility of conformally mapping graph of $x\sin(1/x)$ to $\mathbb{R}$

Published on 22 Mar 2026 - 12:24

score 120 · Answer 5 · 2026-03-20 07:54:45

120

Views

Product of holomorphically convex spaces is again holomorphically convex

Published on 20 Mar 2026 - 7:54

score 246 · Answer 6 · 2026-03-20 04:55:32

246

Views

Prove that $X$ is a Riemann surface using basic definitions

Published on 20 Mar 2026 - 4:55

score 34 · Answer 7 · 2026-03-20 08:13:02

34

Views

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

Published on 20 Mar 2026 - 8:13

score 313 · Answer 8 · 2026-03-21 00:33:37

313

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 21 Mar 2026 - 0:33

score 495 · Answer 9 · 2026-03-22 05:53:03

495

Views

Proving $0$ is a removable singularity

Published on 22 Mar 2026 - 5:53

score 1k · Answer 10 · 2026-03-20 03:51:20

1k

Views

Holomorphic function satisfying $f^{-1}(\Bbb R)=\Bbb R$ is of the form $f(z)=az+b$

Published on 20 Mar 2026 - 3:51

score 599 · Answer 11 · 2026-03-20 09:08:36

599

Views

Is there an entire function satisfying $|f(z)|=|z|+1$ for every $|z|\geq2017$?

Published on 20 Mar 2026 - 9:08

score 180 · Answer 12 · 2026-03-25 01:23:43

180

Views

Show $\overline{f(\overline{z})}$ holomorphic

Published on 25 Mar 2026 - 1:23

score 104 · Answer 13 · 2026-03-25 01:13:14

104

Views

$\Bbb{E}(e^{\lambda X})=e^{\lambda^2/2}$ impliesthat $\Bbb{E}(e^{zX})$ is holomorphic and well-defined.

Published on 25 Mar 2026 - 1:13

score 780 · Answer 14 · 2026-03-23 01:23:50

780

Views

Prove or disprove that every Holomorphic function preserving unboundedness is a polynomial.

Published on 23 Mar 2026 - 1:23

score 492 · Answer 15 · 2026-03-22 18:05:01

492

Views

Holomorphic function mapping unit disc to the "pacman" $U = \{|z|<1,\ \mathrm{Arg}z \notin [-\frac{\pi}{4},\frac{\pi}{4}]\}$

Published on 22 Mar 2026 - 18:05

List Question

order of zero of modular form from it's expansion at infinity

Holomorphic domain of $ \Phi\left(z\right)=\ln\left(\frac{z-a}{z+a}\right)$

Complex Analysis - Harmonic function as real part of holomorphic function

Impossibility of conformally mapping graph of $x\sin(1/x)$ to $\mathbb{R}$

Product of holomorphically convex spaces is again holomorphically convex

Prove that $X$ is a Riemann surface using basic definitions

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

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

Proving $0$ is a removable singularity

Holomorphic function satisfying $f^{-1}(\Bbb R)=\Bbb R$ is of the form $f(z)=az+b$

Is there an entire function satisfying $|f(z)|=|z|+1$ for every $|z|\geq2017$?

Show $\overline{f(\overline{z})}$ holomorphic

$\Bbb{E}(e^{\lambda X})=e^{\lambda^2/2}$ impliesthat $\Bbb{E}(e^{zX})$ is holomorphic and well-defined.

Prove or disprove that every Holomorphic function preserving unboundedness is a polynomial.

Holomorphic function mapping unit disc to the "pacman" $U = \{|z|<1,\ \mathrm{Arg}z \notin [-\frac{\pi}{4},\frac{\pi}{4}]\}$

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