From Richard Lewis
The otherwise excellent article on the Riemann hypothesis omitted an important caveat in the “Zeta and the primes” sidebar (22 March, p 40): namely that the summation form given is appropriate only for numbers whose real part is greater than +1.
Plugging -2, for instance, into the given formula (which almost every reader is going to be tempted to do) gives zeta(-2) = 1 + 4 + 9 + 16…
The sum here is clearly not going anywhere near zero.
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