Question

ind an analytic continuation 𝑓𝑡 ,𝐷𝑡 : 0 ≤ 𝑡 ≤ 1 of

𝑓0

,𝐷0

along 𝛾 and show that 𝑓1

1 = 𝑓0

1

Where 𝐷0 = 𝐵 1 , 1 𝑎𝑛𝑑 𝑓0

is restriction of the principal

branch of 𝑧 to 𝐷0

. 𝛾 𝑡 = 𝑒

2𝜋𝑖𝑡 𝑎𝑛𝑑 𝜎 𝑡 = 𝑒

4𝜋𝑖𝑡