Skip to main content
MathOverflow

Return to Question

clarified title
Link
YCor
YCor
  • 63.9k
  • 5
  • 187
  • 286

fixed Fixed points of a function $z\mapsto\overline{P(z)}$ of a complex variable

added 2 characters in body
Source Link
user159888
user159888
  • 559
  • 4
  • 11

The equation $z^2=\overline{z}$ has four zeros and this example motivates us to generalize the problem to this form; How many zeros does the equation $P(z)=\overline{z}$ have if $P(z)$ is a polynomial of degree $n?$$n>1?$ Can we find the bound for the number of zeros of this problem? The example motivate us to conjecture that it may be at most $2n,$ if not at most $2n+n-2=3n-2.$ I am suggesting mere by intuition! May I request you to share your thoughts on this?

The equation $z^2=\overline{z}$ has four zeros and this example motivates us to generalize the problem to this form; How many zeros does the equation $P(z)=\overline{z}$ have if $P(z)$ is a polynomial of degree $n?$ Can we find the bound for the number of zeros of this problem? The example motivate us to conjecture that it may be at most $2n,$ if not at most $2n+n-2=3n-2.$ I am suggesting mere by intuition! May I request you to share your thoughts on this?

The equation $z^2=\overline{z}$ has four zeros and this example motivates us to generalize the problem to this form; How many zeros does the equation $P(z)=\overline{z}$ have if $P(z)$ is a polynomial of degree $n>1?$ Can we find the bound for the number of zeros of this problem? The example motivate us to conjecture that it may be at most $2n,$ if not at most $2n+n-2=3n-2.$ I am suggesting mere by intuition! May I request you to share your thoughts on this?

Source Link
user159888
user159888
  • 559
  • 4
  • 11

fixed points of a function of a complex variable

The equation $z^2=\overline{z}$ has four zeros and this example motivates us to generalize the problem to this form; How many zeros does the equation $P(z)=\overline{z}$ have if $P(z)$ is a polynomial of degree $n?$ Can we find the bound for the number of zeros of this problem? The example motivate us to conjecture that it may be at most $2n,$ if not at most $2n+n-2=3n-2.$ I am suggesting mere by intuition! May I request you to share your thoughts on this?