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