The Reimann "Zeta" function: How can it ever converge?

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Sujet : The Reimann "Zeta" function: How can it ever converge?
De : gazelle (at) *nospam* shell.xmission.com (Kenny McCormack)
Groupes : sci.math
Date : 25. Mar 2025, 20:15:55
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Organisation : The official candy of the new Millennium
Message-ID : <vruvdb$mo0t$1@news.xmission.com>
User-Agent : trn 4.0-test77 (Sep 1, 2010)
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?

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Date Sujet#  Auteur
25 Mar 25 * The Reimann "Zeta" function: How can it ever converge?5Kenny McCormack
25 Mar 25 +* Re: The Reimann "Zeta" function: How can it ever converge?3efji
26 Mar 25 i`* Thanks! (Was: The Reimann "Zeta" function: How can it ever converge?)2Kenny McCormack
26 Mar 25 i `- Re: Thanks! (Was: The Reimann "Zeta" function: How can it ever converge?)1FromTheRafters
25 Mar 25 `- Re: The Reimann "Zeta" function: How can it ever converge?1FromTheRafters

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