Proving a certain behavior of zeros of an analytic function

121 Views Asked by At

enter image description here

This is an exercise from Conway that I am stuck at. First, how can I use the proposition 5.4 (put below) to prove it? I cannot see how $log$ function can come in. Also I am stuck at (b) too. I know the definition of Blaschke product and I solved the exercise 5.4 mentioned here. But I cannot solve (b)... Could anyone please help me?enter image description here

This is proposition 5.4. enter image description here

This is the exercise 5.4 of the chapter 7 about Blaschke products.