Mathematica 9 is now available
Services & Resources / Wolfram Forums / MathGroup Archive
-----

MathGroup Archive 2010

[Date Index] [Thread Index] [Author Index]

Search the Archive

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

  • To: mathgroup at smc.vnet.net
  • Subject: [mg106813] Re: Calculating zeta(1+it) for t in range of 10^12 accurately
  • From: "Steve Luttrell" <steve at _removemefirst_luttrell.org.uk>
  • Date: Sun, 24 Jan 2010 05:40:07 -0500 (EST)
  • References: <hj130p$bd4$1@smc.vnet.net>

On 
http://reference.wolfram.com/mathematica/note/SomeNotesOnInternalImplementation.html#21479 
it says:

"Zeta and related functions use Euler-Maclaurin summation and functional 
equations. Near the critical strip they also use the Riemann-Siegel 
formula."

-- 
Stephen Luttrell
West Malvern, UK

"Dominic" <miliotodc at rtconline.com> wrote in message 
news:hj130p$bd4$1 at smc.vnet.net...
> 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
>
> 



  • Prev by Date: Re: Crash when using Dot on matrices, v 6.0.2
  • Next by Date: Re: Crash when using Dot on matrices, v 6.0.2
  • Previous by thread: Calculating zeta(1+it) for t in range of 10^12 accurately
  • Next by thread: was Re: More /.{I->-1} craziness. Schools are conservative. So are