How can I make the transition from blue to purple (I do not want the white part) more smooth? When using a gradient node and a color ramp, Even though a gradient should be smooth, I get sharp edges separating the colors in the color ramp. Also, there is this white part that comes out of nowhere. Help! I use blender 2.82 and windows.
In your setup, the emission shader is causing that white strip.  In the pic below, I set it up exactly as you did, but I bypassed the emission shader.