Zeros on the complex plane

  • #1
zetafunction
391
0
given a finite polynomial

[tex] a_{0}+a_{1}x+a_{2}x^{2}+a_{3}x^{3}+............+a_{n}x^{n} =P(x)[/tex]

is there a theorem or similar to ensure that P(x) has NO roots on the left of complex plane defined by [tex] Re(x<0) [/tex] ??
 

Answers and Replies

  • #2
hamster143
908
2
What restrictions do you put on coefficients?

If you put n = 1, a_0 = 1, a_1 = 1, you get a polynomial with a root x=-1 on the left of complex plane right away. Perhaps I did not understand your question?
 
  • #3
Office_Shredder
Staff Emeritus
Science Advisor
Gold Member
2021 Award
5,223
1,178
I think he's asking what conditions make it so there are no roots with real part negative
 
  • #4
hamster143
908
2
Ah! That makes sense.
 
  • #5
Count Iblis
1,859
7
Map the left of the complex plane to the unit disk via a conformal map (you need the möbius map) and then count the zeroes by evaluating the integral of f'/f.
 

Suggested for: Zeros on the complex plane

  • Last Post
Replies
1
Views
386
  • Last Post
Replies
2
Views
618
Replies
2
Views
322
Replies
6
Views
991
  • Last Post
Replies
4
Views
394
Replies
4
Views
836
  • Last Post
Replies
10
Views
783
  • Last Post
Replies
1
Views
416
  • Last Post
Replies
10
Views
914
  • Last Post
Replies
14
Views
2K
Top