Timeline for Lower bounding the multiplicative order of 2 modulo p
Current License: CC BY-SA 3.0
2 events
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| Aug 30, 2015 at 16:28 | comment | added | Vesselin Dimitrov | It is interesting that even raising the exponent $1/2$ in this result by an $\epsilon$ has remained an open problem without the Riemann hypothesis for the Kummer fields. So it seems that the density cannot be improved by much with current technology. (But Pappalardi did manage to prove $\mathrm{ord}_p^{\times}{a} > \sqrt{p} \, \exp(\log^{0.1}(p))$ for a set of primes of full density. Hence we do know that if $\theta \leq 1/2$, the set $\{p : \, \mathrm{ord}_p^{\times}{a} \leq p^{\theta}\}$ actually has density zero.) | |
| Aug 30, 2015 at 11:49 | history | answered | Joe Silverman | CC BY-SA 3.0 |