3D plots

Over the complex z-plane of (zeta;zeta^k-z)_j^-1

The real part of where for various values of and . The surface is colored according to the imaginary part. The right graphic is a contour plot of the scaled real part, meaning the height values of the left graphic translate into color values in the right graphic. Red is smallest and violet is largest.

The absolute value of the real part of where for various values of and . The surface is colored according to the absolute value of the imaginary part. The right graphic is a contour plot of the scaled absolute value of the real part, meaning the height values of the left graphic translate into color values in the right graphic. Red is smallest and violet is largest.

The imaginary part of where for various values of and . The surface is colored according to the real part. The right graphic is a contour plot of the scaled imaginary part, meaning the height values of the left graphic translate into color values in the right graphic. Red is smallest and violet is largest.

The absolute value of the imaginary part of where for various values of and . The surface is colored according to the absolute value of the real part. The right graphic is a contour plot of the scaled absolute value of the imaginary part, meaning the height values of the left graphic translate into color values in the right graphic. Red is smallest and violet is largest.

The absolute value of where for various values of and . The surface is colored according to the argument. The right graphic is a contour plot of the scaled absolute value, meaning the height values of the left graphic translate into color values in the right graphic. Red is smallest and violet is largest.

The argument of where for various values of and . The surface is colored according to the absolute value. The right graphic is a contour plot of the scaled argument, meaning the height values of the left graphic translate into color values in the right graphic. Red is smallest and violet is largest. has lines of discontinuities over the .

The square of the sine of the argument of where for various values of and . For dominantly real values, the function values are near 0, and for dominantly imaginary values, the function values are near 1. The surface is colored according to the absolute value. The right graphic is a cyclically colored contour plot of the argument. Red represents arguments near and light‐blue represents arguments near 0.

The logarithm of the absolute value of where for various values of and in the upper half‐plane. The surface is colored according to the square of the argument. In this plot, zeros are easily visible as spikes extending downwards and poles and logarithmic singularities as spikes extending upwards.

Over the complex z-plane of (zeta;zeta^k-zeta-z)_j^-1

The real part of where for various values of and . The surface is colored according to the imaginary part. The right graphic is a contour plot of the scaled real part, meaning the height values of the left graphic translate into color values in the right graphic. Red is smallest and violet is largest.

The absolute value of the real part of where for various values of and . The surface is colored according to the absolute value of the imaginary part. The right graphic is a contour plot of the scaled absolute value of the real part, meaning the height values of the left graphic translate into color values in the right graphic. Red is smallest and violet is largest.

The imaginary part of where for various values of and . The surface is colored according to the real part. The right graphic is a contour plot of the scaled imaginary part, meaning the height values of the left graphic translate into color values in the right graphic. Red is smallest and violet is largest.

The absolute value of the imaginary part of where for various values of and . The surface is colored according to the absolute value of the real part. The right graphic is a contour plot of the scaled absolute value of the imaginary part, meaning the height values of the left graphic translate into color values in the right graphic. Red is smallest and violet is largest.

The absolute value of where for various values of and . The surface is colored according to the argument. The right graphic is a contour plot of the scaled absolute value, meaning the height values of the left graphic translate into color values in the right graphic. Red is smallest and violet is largest.

The argument of where for various values of and . The surface is colored according to the absolute value. The right graphic is a contour plot of the scaled argument, meaning the height values of the left graphic translate into color values in the right graphic. Red is smallest and violet is largest. has lines of discontinuities over the .

The square of the sine of the argument of where for various values of and . For dominantly real values, the function values are near 0, and for dominantly imaginary values, the function values are near 1. The surface is colored according to the absolute value. The right graphic is a cyclically colored contour plot of the argument. Red represents arguments near and light‐blue represents arguments near 0.

The logarithm of the absolute value of where for various values of and in the upper half‐plane. The surface is colored according to the square of the argument. In this plot, zeros are easily visible as spikes extending downwards and poles and logarithmic singularities as spikes extending upwards.

Over the complex z-plane of (zeta;zeta^k-zeta z-z)_j^-1

The real part of where for various values of and . The surface is colored according to the imaginary part. The right graphic is a contour plot of the scaled real part , meaning the height values of the left graphic translate into color values in the right graphic. Red is smallest and violet is largest.

The absolute value of the real part of where for various values of and . The surface is colored according to the absolute value of the imaginary part. The right graphic is a contour plot of the scaled absolute value of the real part, meaning the height values of the left graphic translate into color values in the right graphic. Red is smallest and violet is largest.

The imaginary part of where for various values of and . The surface is colored according to the real part. The right graphic is a contour plot of the scaled imaginary part, meaning the height values of the left graphic translate into color values in the right graphic. Red is smallest and violet is largest.

The absolute value of the imaginary part of where for various values of and . The surface is colored according to the absolute value of the real part. The right graphic is a contour plot of the scaled absolute value of the imaginary part, meaning the height values of the left graphic translate into color values in the right graphic. Red is smallest and violet is largest.

The absolute value of where for various values of and . The surface is colored according to the argument. The right graphic is a contour plot of the scaled absolute value, meaning the height values of the left graphic translate into color values in the right graphic. Red is smallest and violet is largest.

The argument of where for various values of and . The surface is colored according to the absolute value. The right graphic is a contour plot of the scaled argument, meaning the height values of the left graphic translate into color values in the right graphic. Red is smallest and violet is largest. has lines of discontinuities over the .

The square of the sine of the argument of where for various values of and . For dominantly real values, the function values are near 0, and for dominantly imaginary values, the function values are near 1. The surface is colored according to the absolute value. The right graphic is a cyclically colored contour plot of the argument. Red represents arguments near and light‐blue represents arguments near 0.

The logarithm of the absolute value of where for various values of and in the upper half plane. The surface is colored according to the square of the argument. In this plot, zeros are easily visible as spikes extending downwards and poles and logarithmic singularities as spikes extending upwards.

Over the complex z-plane of various roots along certain directions

The functions where for various and values of and along selected directions of the . The right graphic shows the real parts and the left graphic shows the imaginary parts. At the branch points the curves bifurcate.