Riemann Surfaces (60 graphics)

Riemann surfaces of (zeta;zeta^k-z)_j^-1

The functions , for over the . The left graphic shows and the right graphic shows . The roots , form the Riemann surface of the bivariate polynomial . The point is the unique branch point of these functions.

Riemann surfaces of (zeta;zeta^k-z^k)_j^-1

The functions , for over the . The left graphic shows and the right graphic shows . The roots , form the Riemann surface of the bivariate polynomial . It is split into independent sheets.

Riemann surfaces of (zeta;zeta^k-z^k+1)_j^-1

The functions , for over the . The left graphic shows and the right graphic shows . The roots , form the Riemann surface of the bivariate polynomial . The branch points are the roots of unity.

Riemann surfaces of (zeta;zeta^k-zeta-z)_j^-1

The functions , for over the . The left graphic shows and the right graphic shows . The roots , form the Riemann surface of the bivariate trinomial polynomial .

Riemann surfaces of (zeta;zeta^k-Sum_m=0^kz^m)_j^-1

The functions , for over the . The left graphic shows and the right graphic shows . The roots , form the Riemann surface of the bivariate polynomial .

Riemann surfaces of (zeta;Sum_m=0^kzeta^m-Sum_m=0^kz^m)_j^-1

The functions , for over the . The left graphic shows and the right graphic shows . The roots , form the Riemann surface of the bivariate polynomial .

Riemann surfaces of (zeta;Sum_m=0^kzeta^m-1/Sum_m=0^kz^m)_j^-1

The functions , for over the . The left graphic shows and the right graphic shows . The roots , form the Riemann surface of the bivariate polynomial .

Riemann surfaces of (zeta;Sum_m=0^kzeta^m Sum_m=0^kz^m)_j^-1

The functions , for over the . The left graphic shows and the right graphic shows . The roots , form the Riemann surface of the bivariate polynomial .

Riemann surfaces of various roots

The functions , for various over the . The left graphic shows and the right graphic shows . The roots , form the Riemann surface of the bivariate polynomial .