Timeline for Largest known zero of the Riemann zeta function
Current License: CC BY-SA 4.0
10 events
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| Jan 30, 2022 at 21:16 | history | edited | YCor | CC BY-SA 4.0 |
formatting, added tag
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| Jul 13, 2021 at 17:24 | comment | added | JoshuaZ | I'm confused by question 3. Regarding question 3, that can't happen. RH is equivalent to RH is equivalent to the error term being $O(x^{\frac{1}{2} + \epsilon})$. But RH also implies a stronger result . Namely that $|\pi(x) - \operatorname{li}(x)| < \frac{1}{8\pi} \sqrt{x} \log x$ for $x \geq 2657$ (due to Schoenfeld). But the upshot is that your suggested error size would still imply RH. | |
| Jul 13, 2021 at 17:08 | answer | added | Mats Granvik | timeline score: 1 | |
| Mar 6, 2021 at 17:15 | comment | added | Geoffrey Irving | As an aside, your conditional statement that “RH won't be disproved by a computer before the sun becomes a red giant” implicitly assumes that brute force is the only approach available to a computer. | |
| Aug 3, 2017 at 21:01 | comment | added | Will Sawin | For Question 3, doesn't that error term imply the full Riemann hypothesis? | |
| Aug 3, 2017 at 20:54 | answer | added | Stopple | timeline score: 17 | |
| Mar 8, 2017 at 16:44 | answer | added | joro | timeline score: 4 | |
| Mar 8, 2017 at 16:01 | comment | added | Timothy Chow | If you are not already aware of it, Odlyzko's papers here are relevant: dtc.umn.edu/~odlyzko/unpublished/index.html In view of Odlyzko's work, I'm not sure that "largest known zero" is the right concept to ask about since Odlyzko's methods allow one to "jump" to a large imaginary value and compute zeros around that point, precisely to investigate the kinds of questions you pose here. I recall that Odlyzko is agnostic about RH, and part of his reasoning is that, as you suggest here, he finds it quite possible that RH will fail at some point beyond our computational reach. | |
| Mar 8, 2017 at 10:36 | history | edited | Bazin | CC BY-SA 3.0 |
added 16 characters in body
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| Mar 8, 2017 at 10:24 | history | asked | Bazin | CC BY-SA 3.0 |