Extremal polynomials in Dirichlet-type spaces

Left to right: combined zero sets for Taylor polynomials, Cesaro polynomials, and Riesz polynomials, up to degree 50, approximating 1/f.

For background, consult my paper with Bénéteau, Condori, Liaw, and Seco in J. Anal. Math. (to appear).

f=1-z:
f=1-z+z^2
f=(1-z)^2
f=1+z^2