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

riemann

asked 5 years ago

Rami Rami
21 ●3

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 ( 5 years ago )

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 ( 5 years ago )

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

Iguananaut ( 5 years ago )

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answered 4 years ago

fredrik
136 ●4 ●7

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: 5 years ago

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Last updated: Mar 29 '21

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