html, body, form { margin: 0; padding: 0; width: 100%; } #calculate { position: relative; width: 177px; height: 110px; background: transparent url(/images/alphabox/embed_functions_inside.gif) no-repeat scroll 0 0; } #i { position: relative; left: 18px; top: 44px; width: 133px; border: 0 none; outline: 0; font-size: 11px; } #eq { width: 9px; height: 10px; background: transparent; position: absolute; top: 47px; right: 18px; cursor: pointer; }

 Root

Riemann Surfaces (60 graphics)

Riemann surfaces of (zeta;zetak-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;zetak-zk)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;zetak-zk+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;zetak-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;zetak-Summ=0kzm)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;Summ=0kzetam-Summ=0kzm)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;Summ=0kzetam-1/Summ=0kzm)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;Summ=0kzetam Summ=0kzm)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 .