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MathGroup Archive 2004

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NewtonZero never comes down

  • To: mathgroup at
  • Subject: [mg51416] NewtonZero never comes down
  • From: Roger Bagula <tftn at>
  • Date: Sat, 16 Oct 2004 04:21:07 -0400 (EDT)
  • Reply-to: tftn at
  • Sender: owner-wri-mathgroup at

I've tried several ways to find better values for
zeta zeros fast and easy...
FindRoot[] just doesn't give much accuracy.
NewtonZero[] tends to just spin it's wheels on my machine....
Here's what I came up with that gets about 20 places
and pretty fast relatively.
It's much better than FindRoot[] anyway!
The zeta zeros all seem to be transcendental irrational numbers
and are harder to calculate than most numbers in modern number theory.

(* finding Zeta Zero roots*)
(* using approximation from analyitic continuation on 0<=z<=1 strip 
where zeta dosesn't converge*)
t=(2 Sqrt[2])*25*Pi^2*Sqrt[n]/(6*Sqrt[Digits])-16
(* gives the zeta zeros given in Jahnke-Emde Tables of Functions, Dover*)
(* definition of Newton function*)
(* ten iterations toward the zero*)
(* values starting at the continuation values approximated*)

Respectfully, Roger L. Bagula

tftn at, 11759Waterhill Road, Lakeside,Ca 92040-2905,tel: 619-5610814 :
alternative email: rlbtftn at

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