Sunday, May 29, 2016

How is $zeta(0)=-1/2$?







Fermat's Dream by Kato et al. gives the following:





  1. $\zeta(s)=\sum\limits_{n=1}^{\infty}\frac{1}{n^s}$ (the standard Zeta function) provided the sum converges.


  2. $\zeta(0)=-1/2$




Thus, $1+1+1+...=-1/2$ ? How can this possibly be true? I guess I'm under the impression that $\sum 1$ diverges.

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