Question

Find 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

Answer 1

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