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Re: Riemann zeta function conundrum
Posted:
Feb 24, 1998 12:06 AM


In article <01bd40b8$909e3750$ae9deac2@karihnt>, "Kari HyvÃÂÃÂ¶nen" <karhyv@icenet.fi> wrote:
=> Using the identity x^ns1=(x^s1)sum(x^ks), n is integer, and the product => form of Riemann zeta function: zeta(s)=1/product(1p^s) over all primes p,
which converges only for real part of s exceeding 1,
=> I get zeta(ns)=1/product(1p^ns)=1/[product(1p^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)



