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Calculating zeta(1+it) for t in range of 10^12 accurately

  • To: mathgroup at smc.vnet.net
  • Subject: [mg106611] Calculating zeta(1+it) for t in range of 10^12 accurately
  • From: "Dominic" <miliotodc at rtconline.com>
  • Date: Mon, 18 Jan 2010 02:36:02 -0500 (EST)

Hello guys.  I am working on a project which requires me to calculate 
zeta(1+it) for t in the range no more than 10^12 and it's in 
arbitrary-precision format like:

t=(Pi 10^12)/Log(3) -1/3;

What is the best way to make sure I'm getting the accuracy correctly to 
at least 6 decimal places?  I've been using:

N[Zeta[1+it],{Infty,20}]

Is this the best way?  Also, can anyone tell me what algorithm 
Mathematica is using to calculate zeta at this value?  Is it 
Riemann-Segel?

Thanks,

Dominic



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