Timeline for Chowla's Construction of prime having least quadratic non-residue $\gg \log p$
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
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| Jul 16, 2016 at 16:46 | comment | added | xyz | @ThomasBloom yes I am satisfied with the comments but how do i accept until post it as an Answer | |
| Jul 16, 2016 at 15:38 | comment | added | Thomas Bloom | Montgomery showed that conditional on GRH there are infinitely many primes $p$ such that $n(p)\gg \log p \log \log p$. | |
| Jul 14, 2016 at 20:31 | comment | added | Felipe Voloch | There is a somewhat vague discussion in Bach and Sorensen, Math Comp 65 (1996) bottom of pg 1718. I've seen it in other places too, but I don't recall a specific reference. | |
| Jul 14, 2016 at 19:10 | comment | added | xyz | @FelipeVoloch can you give any reference for the conjecture $n(p)=O((\log p)^{1+\epsilon})$. | |
| Jul 14, 2016 at 18:31 | comment | added | Felipe Voloch | Under GRH $n(p) = O((\log p)^2)$ and, conjecturally $n(p) = O((\log p)^{1+\epsilon}), \forall \epsilon > 0$. | |
| Jul 14, 2016 at 18:19 | comment | added | xyz | I found this paper by Graham and Ringrose which proved that there are infinitely many primes $p$ such that the least quadratic nonresidue $n(p)$ satisfies $n(p) \gg \log p \log \log \log p $. But still now my question is does it removes the possibility of proving n(p) = O(\log p \log \log \log p) | |
| Jul 14, 2016 at 15:07 | review | First posts | |||
| Jul 14, 2016 at 15:18 | |||||
| Jul 14, 2016 at 15:02 | history | asked | xyz | CC BY-SA 3.0 |