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Lewi_Sol
Lewi_Sol
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Suppose $f(z)=c_1z+c_2z^2+\cdots+c_nz^n$ is a univalent map on the unit disk.

You may assume $c_1=1$. All coefficients are complex.

Is there a sharp bound on the modulus of the last coefficient $c_n$? 

How about the other coefficients?

Suppose $f(z)=c_1z+c_2z^2+\cdots+c_nz^n$ is a univalent map on the unit disk.

You may assume $c_1=1$. All coefficients are complex.

Is there a sharp bound on the last coefficient $c_n$? How about the other coefficients?

Suppose $f(z)=c_1z+c_2z^2+\cdots+c_nz^n$ is a univalent map on the unit disk.

You may assume $c_1=1$. All coefficients are complex.

Is there a sharp bound on the modulus of the last coefficient $c_n$? 

How about the other coefficients?

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Lewi_Sol
Lewi_Sol
  • 309
  • 2
  • 9

Bounds on coefficients: univalent maps

Suppose $f(z)=c_1z+c_2z^2+\cdots+c_nz^n$ is a univalent map on the unit disk.

You may assume $c_1=1$. All coefficients are complex.

Is there a sharp bound on the last coefficient $c_n$? How about the other coefficients?