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