G
Topic
First Poster
Last Poster
Construct Riemann Map
Mr.Trick 0
Source: Homework
Construct an explicit biholomorphism between 
and 
.
and 
.
0 replies
Prove the Great Picard Theorem(meromorphic func) with the Little Picard Theorem
wyz 3
N
by GreenKeeper
Theorem 1 (The Little Picard theorem) If 
is an entire function on 
, then either 
or 
.
Theorem 2 (The Great Picard Thm.)(Meromorphic function edition) If
is an meromorphic function on , then either or 
.
Please prove Theorem 2 with Theorem 1
thanks for your help
is an entire function on 
, then either 
or 
.Theorem 2 (The Great Picard Thm.)(Meromorphic function edition) If
is an meromorphic function on , then either or 
.Please prove Theorem 2 with Theorem 1
thanks for your help
3 replies
where 
is the circle 
.
Contour Integration
pokoknyaakuimut 1
N
by removablesingularity
Source: Indonesian Undergraduate MO
Given a complex polynomial 
and a contour 
in positive direction. If all roots of are inside 
and 
where 
, then find the value of 
.
and a contour 
in positive direction. If all roots of are inside 
and 
where 
, then find the value of 
.
1 reply
find all pairs
Peter 3
N
by lifeismathematics
Source: IMC 2000 day 1 problem 2
Let 
and 
, Find al pairs 
, 
for which 
.
and 
, Find al pairs 
, 
for which 
.
3 replies
has infinite roots
Complex Analysis Problem
artificial 1
N
by The.survivor
, what is the Laurent expansion at 
about punctured disk 
up to and including the term 
and what is the residue of 
at
1 reply
Question about Riemann Hypothesis
hashtagmath 11
N
by greenturtle3141
I am just learning about the Riemann Hypothesis and a question that has been nagging me is why can't we just find the zeroes of the functional equation and see if it holds against the hypothesis? It seems to me that finding the zeroes of that equations would easily prove/disprove the hypothesis. But obviously, it's more complex (no pun intended) than that. Can someone provide a glimpse into the difficulty of the problem?
Thanks again :D
Thanks again :D
11 replies
complex roots of polynomial and inequality for coefficients
su7e 5
N
by XbenX
polynomial ![$P(z)=a_nz^n+\dots+ a_1z+a_0\in\mathbb{R}[x]$](//latex.artofproblemsolving.com/2/8/2/282e6ec448acd71777851a7200890186cd310b93.png)
, 
, has all complex roots in a set 
.
show that
for 
.
![$P(z)=a_nz^n+\dots+ a_1z+a_0\in\mathbb{R}[x]$](http://latex.artofproblemsolving.com/2/8/2/282e6ec448acd71777851a7200890186cd310b93.png)
, 
, has all complex roots in a set 
.show that
for 
.
5 replies
triangle
123... 1
N
by 277546
Supose 
are the vertices of closed equilateral triangle in the plane,
find the maximum value of
where 
range over this triangle.
are the vertices of closed equilateral triangle in the plane,find the maximum value of
where 
range over this triangle.
1 reply
