The function,Originally Posted by naty
Defined as is not a homomorphism because,
thus,
thus,
Only true when . Thus it is not an automorphism.
Similarily,
Gives,
Only true for .
I need to prove, that f is holomorphic automorphism C*=C\{0}
ONLY when it's formation is
f_a(z)=az
or
f_a(z)=a/z
for some non-zero complex number a.
How do I get to this formation of f if I know that f is holomorphic automorphism C*=C\{0}?