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How can I calculate Riemann zeta function for large imaginary parts?

asked 2019-12-14 20:30:01 +0200

Rami Rami gravatar image

I tried to calculate it for some complex number with imaginary part more than 10^19 but it didn't work out.

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How did you try it, and in what way did it not "work out"?

Iguananaut gravatar imageIguananaut ( 2019-12-16 15:03:49 +0200 )edit

I tried to calculate it on Sage Cell Server. I wrote zeta(0.5+40000000000000000000*I) and clicked evaluate, then it said there is overflow.

Rami Rami gravatar imageRami Rami ( 2019-12-17 12:35:55 +0200 )edit

It seems PARI simply can't handle such a large number. Does anyone have any other ideas?

Iguananaut gravatar imageIguananaut ( 2019-12-23 16:21:52 +0200 )edit

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answered 2021-03-29 20:37:14 +0200

fredrik gravatar image

This 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
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Asked: 2019-12-14 20:30:01 +0200

Seen: 319 times

Last updated: Mar 29 '21