Question

Extending a holomorphic function $\mathbb{C} \rightarrow \mathbb{C}$ to be holomorphic on the Riemann sphere $\mathbb{C}^{*}$

score 190 · Answer 1 · 2023-05-20 14:26:02

190

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Extending a holomorphic function $\mathbb{C} \rightarrow \mathbb{C}$ to be holomorphic on the Riemann sphere $\mathbb{C}^{*}$

Published on 20 May 2023 - 14:26

score 57 · Answer 2 · 2023-05-25 02:34:21

Suppose $f(z)$ is meromorphic on $\mathbb C$, and there are two circles $K, K'$, so that $f(K)⊂K'$, prove that $f(z)$ is a rational function.

score 38 · Answer 3 · 2023-05-26 16:19:58

38

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Advantage of an alternative formula for complex gamma function

Published on 26 May 2023 - 16:19

score 32 · Answer 4 · 2023-06-22 21:27:54

32

Views

Looking for a specific zeta function.

Published on 22 Jun 2023 - 21:27

score 33 · Answer 5 · 2023-06-23 18:04:15

33

Views

Showing that a meromorphic function has a dense range in a punctured disk with a non-isolated singularity

Published on 23 Jun 2023 - 18:04

score 39 · Answer 6 · 2023-08-09 17:30:19

39

Views

Does the order of vanishing at infinity for an automorphic form depend on the chosen period?

Published on 09 Aug 2023 - 17:30

score 139 · Answer 7 · 2023-09-18 08:26:42

139

Views

Every holomorphic map into Riemann sphere is meromorphic

Published on 18 Sep 2023 - 8:26

score 145 · Answer 8 · 2023-10-12 07:52:19

145

Views

An automorphic function with no poles is constant.

Published on 12 Oct 2023 - 7:52

score 38 · Answer 9 · 2023-10-12 16:16:54

38

Views

Quotient of meromorphic functions

Published on 12 Oct 2023 - 16:16

score 13 · Answer 10 · 2023-10-23 15:25:34

13

Views

Limit of X(s)X(s)/(X(s)-X(s)) as X(s) approaches zero for Meromorphic X(s)

Published on 23 Oct 2023 - 15:25

score 54 · Answer 11 · 2023-11-20 17:29:50

54

Views

Complex function with specific residues

Published on 20 Nov 2023 - 17:29

score 52 · Answer 12 · 2023-11-22 16:07:27

52

Views

Transcendence of meromorphic function vs formal power series

Published on 22 Nov 2023 - 16:07

score 20 · Answer 13 · 2023-12-01 07:19:09

20

Views

Meromorphic infinite product mapping upper half-plane to itself

Published on 01 Dec 2023 - 7:19

score 24 · Answer 14 · 2023-12-06 07:23:27

24

Views

Holomorphic function on unit disc with specific properties

Published on 06 Dec 2023 - 7:23

score 27 · Answer 15 · 2023-12-19 01:26:55

27

Views

On the topic of Exercise 14.4 question 9 in Analytic Function Theory Vol. II by Einar Hille

Published on 19 Dec 2023 - 1:26

List Question

Extending a holomorphic function $\mathbb{C} \rightarrow \mathbb{C}$ to be holomorphic on the Riemann sphere $\mathbb{C}^{*}$

Suppose $f(z)$ is meromorphic on $\mathbb C$, and there are two circles $K, K'$, so that $f(K)⊂K'$, prove that $f(z)$ is a rational function.

Advantage of an alternative formula for complex gamma function

Looking for a specific zeta function.

Showing that a meromorphic function has a dense range in a punctured disk with a non-isolated singularity

Does the order of vanishing at infinity for an automorphic form depend on the chosen period?

Every holomorphic map into Riemann sphere is meromorphic

An automorphic function with no poles is constant.

Quotient of meromorphic functions

Limit of X(s)X(s)/(X(s)-X(s)) as X(s) approaches zero for Meromorphic X(s)

Complex function with specific residues

Transcendence of meromorphic function vs formal power series

Meromorphic infinite product mapping upper half-plane to itself

Holomorphic function on unit disc with specific properties

On the topic of Exercise 14.4 question 9 in Analytic Function Theory Vol. II by Einar Hille

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