I need to prove, that f is holomorphic automorphism C*=C\{0}, when

it's formation is

fa(z)=az

or

fa(z)=a/z

for some non-zero complex number a.

Can anybody help me?

Thank you...

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- Jun 2nd 2006, 01:16 AMnatyHolomorphic automorphism
I need to prove, that f is holomorphic automorphism C*=C\{0}, when

it's formation is

fa(z)=az

or

fa(z)=a/z

for some non-zero complex number a.

Can anybody help me?

Thank you... - Jun 3rd 2006, 07:21 PMThePerfectHackerQuote:

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 . - Jun 5th 2006, 07:36 AMnatyholomorphic automorphism C*=C\{0}
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}? - Jun 5th 2006, 12:18 PMThePerfectHackerQuote:

Originally Posted by**naty**