Timeline for Heuristic model for Lehmer pairs?
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 17, 2022 at 21:30 | comment | added | Agno | @Stopple ARB is an impressive C library for arbitrary-precision ball arithmetic (arblib.org). It has just celebrated its 10th anniversary: fredrikj.net/blog/2022/04/arb-is-10 It has for instance been used in the Polymath 15 project bringing the DBN upper bound down to 0.22, and also more recently by Dave Platt and Tim Trudgian to verify the Riemann hypothesis to record height (bringing the DBN constant to < 0.2). | |
| Apr 16, 2022 at 18:49 | comment | added | Stopple | @Agno Cool! What is ARB? | |
| Apr 14, 2022 at 22:05 | comment | added | Agno | @Stopple A few months ago, I've read your nice paper about the Strong Lehmer pair definition and used it to compute all Strong Lehmer pairs amongst the first 500K non-trivial zeros (there are 3583 pairs). In case people are interested, the csv-data can be found here: drive.google.com/file/d/1Zoxq40LJt87pvl7pN4C1kh-sXkBXdbUP/… with layout: $n, \Im(\rho_n), n+1, \Im(\rho_{n+1}), \Delta(\Im(\rho)), 8 < x < 42/5, 2\Im(\rho_n), 2\Im(\rho_{n+1}), 2\Delta(\Im(\rho))$. Computations were done in ARB. | |
| Apr 14, 2022 at 19:24 | comment | added | Stopple | @SamHopkins Yes it's a single inequality, but it involves every zero of $\zeta(s)$, not just the two in the pair. I would love to see a simple heuristic. With this goal in mind, in 'Lehmer pairs revisited', I defined 'strong Lehmer pairs' and showed every strong Lehmer pair is a Lehmer pair. The hope was that with a more useful definition, it might be possible to show there are infinitely many. | |
| Apr 14, 2022 at 16:43 | comment | added | Sam Hopkins | FWIW, Wikipedia has a pretty simple definition: en.wikipedia.org/wiki/Lehmer_pair | |
| Apr 14, 2022 at 16:34 | history | answered | Stopple | CC BY-SA 4.0 |