Cody Problem 45988 involved computing the Riemann zeta function for real arguments greater than 1. Code that works for that problem can reveal the connection between π and the values of the zeta function evaluated at positive even integers; this connection is explored in Cody Problem 45939. However, to test the Riemann hypothesis--that all non-trivial zeros of the zeta function have a real part of 1/2, one needs to compute the zeta function for complex arguments.
Write a function to evaluate the zeta function for complex arguments.
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why is ζ(2)= pi^2/6 and not 1.644?
Nikolaos, ζ(2)= pi^2/6 = 1.644934066848226