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Topic: Riemann zeta function conundrum
Replies: 3   Last Post: Feb 24, 1998 4:49 PM

 Messages: [ Previous | Next ]
 Gerry Myerson Posts: 192 Registered: 12/8/04
Re: Riemann zeta function conundrum
Posted: Feb 24, 1998 12:06 AM

In article <01bd40b8\$909e3750\$ae9deac2@karihnt>, "Kari HyvÃÂÃÂ¶nen"
<karhyv@icenet.fi> wrote:

=> Using the identity x^ns-1=(x^s-1)sum(x^ks), n is integer, and the product
=> form of Riemann zeta function: zeta(s)=1/product(1-p^-s) over all primes p,

which converges only for real part of s exceeding 1,

=> I get zeta(ns)=1/product(1-p^-ns)=1/[product(1-p^-s)*product(sum(x^-ks)]
=> =zeta(s)/product(sum(x^-ks). Particularly, if zeta(s)=0 => zeta(ns)=0.

which is not a problem, since the zeta function doesn't vanish at s
if the real part of s exceeds 1.

Gerry Myerson (gerry@mpce.mq.edu.au)

Date Subject Author
2/23/98 Kari HyvÃÂ¶nen
2/24/98 Gerry Myerson
2/24/98 R.J.Chapman
2/24/98 Kari HyvÃÂ¶nen