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From: FromTheRafters <FTR@nomail.afraid.org>
Newsgroups: sci.math
Subject: Re: The Reimann "Zeta" function: How can it ever converge?
Date: Tue, 25 Mar 2025 16:58:28 -0400
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Kenny McCormack was thinking very hard :
> So I was reading in Wikipedia about the Zeta function, which is defined as:
>
>     Z(s) = 1/(1**s) + 1/(2**s) + 1/(3**s) + ...
>
> Both the domain and range are specified as the complex numbers.
>
> And it says that if s is a negative integers (-2, -4, -6, etc), then Z(s)
> is zero.  But that can't be right.  But first, a little manipulation:
>
> Suppose s is -2:
>
>     1/(n**s), where s = -2
>
> is:
>
>     1/(1/(n**2))
>
> is:
>
>     n**2
>
> so, the sum is like:
>
>     1+4+9+16+25+...
>
> Which just grows without bounds.  And is certainly never zero.
>
> So, is Wikipedia wrong?  Or just a typo?

It refers to the trivial zeroes of the function. I don't get the double 
asterisk's meaning.