## Infinite zeroes proof

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• Anybody seen this before? http://www.geocities.com/rze17/zeros.pdf (home page http://www.geocities.com/rze17/math.html) Jon Perry perry@globalnet.co.uk
Message 1 of 5 , Feb 28, 2003
• I m looking at the proof for if I could find a flaw. The only thing I have observed is that he took off the null roots of the polynomial, and I was wondering
Message 2 of 5 , Feb 28, 2003
I'm looking at the proof for if I could find a flaw.

The only thing I have observed is that he took off the null roots of the polynomial, and I was wondering if the zeta function had any zero root or not (if they were infinite, then the proof is not valid).

I went to Mathworld and find this equality:

zeta(1-s) = 2· (2pi)^(-s) · cos(1/2 · s · pi) · gamma(s) · zeta(s)

I thought that "If s=1 then zeta(1-s) = zeta(0) = .... · cos(pi/2) = 0." but I have just realised that zeta(1) is the harmonic series! And then the value is in principle indetermined... can anyone say?

What happens if we quit a zero root? zeta(1-s)/s = 2· (2pi)^(-s) · cos(1/2 · s · pi) · gamma(s) · zeta(s) /s ... and then evaluate in s=1 again...

and I'd apply the L'Hôpital rule if I knew how to derivate zeta(1-s) - the s in the denominator is carried out -.

If it can have an infinity of zero roots, and then the proof is not rigorous.

Regards. Jose Brox.

----- Original Message -----
From: Jon Perry
To: Prime Numbers
Sent: Friday, February 28, 2003 5:31 PM

Anybody seen this before?

http://www.geocities.com/rze17/zeros.pdf

Jon Perry
perry@...
http://www.users.globalnet.co.uk/~perry/maths/
BrainBench MVP for HTML and JavaScript
http://www.brainbench.com

Unsubscribe by an email to: primenumbers-unsubscribe@yahoogroups.com
The Prime Pages : http://www.primepages.org/

[Non-text portions of this message have been removed]
• Well, in the same page of Mathworld (http://mathworld.wolfram.com/RiemannZetaFunction.html) we can see the graphic of zeta(x) and it isn t zero in x=0, so
Message 3 of 5 , Feb 28, 2003
Well, in the same page of Mathworld (http://mathworld.wolfram.com/RiemannZetaFunction.html)
we can see the graphic of zeta(x) and it isn't zero in x=0, so forget my previous message.

Jose.

----- Original Message -----
From: Jose Ramón Brox
To: Prime Numbers
Sent: Friday, February 28, 2003 6:30 PM
Subject: Re: [PrimeNumbers] Infinite zeroes proof

I'm looking at the proof for if I could find a flaw.

The only thing I have observed is that he took off the null roots of the polynomial, and I was wondering if the zeta function had any zero root or not (if they were infinite, then the proof is not valid).

I went to Mathworld and find this equality:

zeta(1-s) = 2· (2pi)^(-s) · cos(1/2 · s · pi) · gamma(s) · zeta(s)

I thought that "If s=1 then zeta(1-s) = zeta(0) = .... · cos(pi/2) = 0." but I have just realised that zeta(1) is the harmonic series! And then the value is in principle indetermined... can anyone say?

What happens if we quit a zero root? zeta(1-s)/s = 2· (2pi)^(-s) · cos(1/2 · s · pi) · gamma(s) · zeta(s) /s ... and then evaluate in s=1 again...

and I'd apply the L'Hôpital rule if I knew how to derivate zeta(1-s) - the s in the denominator is carried out -.

If it can have an infinity of zero roots, and then the proof is not rigorous.

Regards. Jose Brox.

----- Original Message -----
From: Jon Perry
To: Prime Numbers
Sent: Friday, February 28, 2003 5:31 PM

Anybody seen this before?

http://www.geocities.com/rze17/zeros.pdf

Jon Perry
perry@...
http://www.users.globalnet.co.uk/~perry/maths/
BrainBench MVP for HTML and JavaScript
http://www.brainbench.com

Unsubscribe by an email to: primenumbers-unsubscribe@yahoogroups.com
The Prime Pages : http://www.primepages.org/

[Non-text portions of this message have been removed]

Unsubscribe by an email to: primenumbers-unsubscribe@yahoogroups.com
The Prime Pages : http://www.primepages.org/

[Non-text portions of this message have been removed]
• I knew of the use of Euler-Maclaurin in Sondow, Jonathan The Riemann hypothesis, simple zeros and the asymptotic convergence degree of improper Riemann sums.
Message 4 of 5 , Feb 28, 2003
I knew of the use of Euler-Maclaurin in

Sondow, Jonathan
The Riemann hypothesis, simple zeros and the asymptotic
convergence degree of improper Riemann sums.
Proc. Amer. Math. Soc. 126 (1998), no. 5, 1311--1314.

It is not clear to me what is added to that by