For a positive integer p, consider the holomorphic function
for
For which values of p does there exist a holomorphic function g ∶ \{0} → such that f(z) = g'(z) for z ∈ \{0}?

Question

Question

This question was previously asked in

CSIR-UGC (NET) Mathematical Science: Held on (26 Nov 2020)

Answer 1

Concept:

A function f(z) is said to be holomorphic in a domain D if f(z) has no singularities in D.

Explanation:

g'(z) = z ∈ \{0}

⇒ g'(z) =

Integrating both sides we get

g(z) =

So g(z) can not be holomorphic if p is a multiple of 2, 3 and 4.

∴ Options (1), (3) and (4) are not correct.

Hence option (2) is correct

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