Timeline for Quadratic residue problem involving prime divisors of a polynomial
Current License: CC BY-SA 4.0
11 events
| when toggle format | what | by | license | comment | |
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| Apr 22, 2023 at 5:24 | comment | added | Gerry Myerson | I'd appreciate it if someone would post an answer (based on the comments). | |
| Apr 21, 2023 at 15:22 | comment | added | Jack | @GHfromMO that is so much simpler, thank you! | |
| Apr 21, 2023 at 15:21 | comment | added | Jack | @Wojowu thanks, that makes sense. | |
| Apr 21, 2023 at 6:02 | comment | added | GH from MO | I should add that for the correct (positive) logarithmic density of splitting primes one does not need Chebotarev. One simply needs that the Dedekind zeta function has a simple pole at $s=1$, then take the logarithmic derivative, and observe that non-splitting primes only contribute $O(1)$ around $s=1$. | |
| Apr 21, 2023 at 3:40 | comment | added | Wojowu | Just the identity. A prime with trivial Frobenius in that compositum will have trivial Frobenius in both subfields, which implies the respective conditions. | |
| Apr 21, 2023 at 3:29 | history | edited | Jack | CC BY-SA 4.0 |
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| Apr 21, 2023 at 3:28 | comment | added | Jack | @Wojowu yes, that's what I mean for 2. I edited the question, thanks. Would you mind expanding a bit on your answer? If $K$ is the composite field, then what would the conjugation invariant subset $X$ of $Gal(K/\mathbb{Q})$ that I apply Chebotarev to be? | |
| Apr 20, 2023 at 23:15 | comment | added | Wojowu | With 2 you mean that there is a root of $f$ modulo $p$? You get a positive answer by applying Chebotarev to the compositum of the splitting field of $f$ and $\Bbb Q(\sqrt{-n})$. | |
| Apr 20, 2023 at 23:08 | history | edited | Jack | CC BY-SA 4.0 |
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| S Apr 20, 2023 at 23:07 | review | First questions | |||
| Apr 21, 2023 at 1:16 | |||||
| S Apr 20, 2023 at 23:07 | history | asked | Jack | CC BY-SA 4.0 |