Editing Hadamard three-circle theorem (section)

==Proof==
The three circles theorem follows from the fact that for any real ''a'', the function Re log(''z''<sup>''a''</sup>''f''(''z'')) is harmonic between two circles, and therefore takes its maximum value on one of the circles. The theorem follows by choosing the constant ''a'' so that this [[harmonic function]] has the same maximum value on both circles.

The theorem can also be deduced  directly from [[Hadamard three-line theorem|Hadamard's three-line theorem]].<ref>{{harvnb|Ullrich|2008}}</ref>