ASKSAGE: Sage Q&A Forum - RSS feedhttps://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Mon, 29 Mar 2021 20:37:14 +0200How can I calculate Riemann zeta function for large imaginary parts?https://ask.sagemath.org/question/49035/how-can-i-calculate-riemann-zeta-function-for-large-imaginary-parts/ I tried to calculate it for some complex number with imaginary part more than 10^19 but it didn't work out.Sat, 14 Dec 2019 20:30:01 +0100https://ask.sagemath.org/question/49035/how-can-i-calculate-riemann-zeta-function-for-large-imaginary-parts/Comment by Iguananaut for <p>I tried to calculate it for some complex number with imaginary part more than 10^19 but it didn't work out.</p>
https://ask.sagemath.org/question/49035/how-can-i-calculate-riemann-zeta-function-for-large-imaginary-parts/?comment=49132#post-id-49132It seems PARI simply can't handle such a large number. Does anyone have any other ideas?Mon, 23 Dec 2019 16:21:52 +0100https://ask.sagemath.org/question/49035/how-can-i-calculate-riemann-zeta-function-for-large-imaginary-parts/?comment=49132#post-id-49132Comment by Iguananaut for <p>I tried to calculate it for some complex number with imaginary part more than 10^19 but it didn't work out.</p>
https://ask.sagemath.org/question/49035/how-can-i-calculate-riemann-zeta-function-for-large-imaginary-parts/?comment=49048#post-id-49048How did you try it, and in what way did it not "work out"?Mon, 16 Dec 2019 15:03:49 +0100https://ask.sagemath.org/question/49035/how-can-i-calculate-riemann-zeta-function-for-large-imaginary-parts/?comment=49048#post-id-49048Comment by Rami Rami for <p>I tried to calculate it for some complex number with imaginary part more than 10^19 but it didn't work out.</p>
https://ask.sagemath.org/question/49035/how-can-i-calculate-riemann-zeta-function-for-large-imaginary-parts/?comment=49057#post-id-49057I tried to calculate it on Sage Cell Server. I wrote zeta(0.5+40000000000000000000*I) and clicked evaluate, then it said there is overflow.Tue, 17 Dec 2019 12:35:55 +0100https://ask.sagemath.org/question/49035/how-can-i-calculate-riemann-zeta-function-for-large-imaginary-parts/?comment=49057#post-id-49057Answer by fredrik for <p>I tried to calculate it for some complex number with imaginary part more than 10^19 but it didn't work out.</p>
https://ask.sagemath.org/question/49035/how-can-i-calculate-riemann-zeta-function-for-large-imaginary-parts/?answer=56425#post-id-56425This is doable but takes a bit of time:
sage: %time u = CBF(0.5+40000000000000000000*I).zeta()
CPU times: user 30min 49s, sys: 113 ms, total: 30min 49s
Wall time: 30min 51s
sage: u
[1.572198667701050 +/- 7.12e-16] + [1.946758000953464 +/- 5.17e-16]*I
Mon, 29 Mar 2021 20:37:14 +0200https://ask.sagemath.org/question/49035/how-can-i-calculate-riemann-zeta-function-for-large-imaginary-parts/?answer=56425#post-id-56425