Can Riemann zeta function be written as ##f(s)=u(s)+iv(s)##?

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SUMMARY

The Riemann zeta function can be expressed in the form of f(s) = u(s) + iv(s), where u(s) and v(s) represent the real and imaginary components, respectively. While every complex-valued function can be decomposed in this manner, the utility of such a representation for the Riemann zeta function is questionable. The discussion emphasizes that the mere ability to express the function in this format does not imply practical significance or application.

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Adel Makram
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I don't recall that I have seen Riemann zeta function put in the form of ##f(s)=u(s)+iv(s)##.
 
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Every complex-valued function can be written that way, but that doesn't mean it has to be useful.
 

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