Riemann Surfaces 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}zetaz)_{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}^{k}z^{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}^{k}zeta^{m}Sum_{m=0}^{k}z^{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}^{k}zeta^{m}1/Sum_{m=0}^{k}z^{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}^{k}zeta^{m} Sum_{m=0}^{k}z^{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 .
