Timeline for Discriminant of numerator of inverse logarithmic derivative operator iteration
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 29, 2018 at 14:07 | vote | accept | Alexander Kalmynin | ||
| Mar 29, 2018 at 12:54 | vote | accept | Alexander Kalmynin | ||
| Mar 29, 2018 at 12:56 | |||||
| Mar 29, 2018 at 12:51 | vote | accept | Alexander Kalmynin | ||
| Mar 29, 2018 at 12:54 | |||||
| Mar 29, 2018 at 12:34 | answer | added | Joe Silverman | timeline score: 10 | |
| Mar 27, 2018 at 20:10 | comment | added | Joe Silverman | @SylvainJULIEN In fact, it seems that $f_n(x)\mid f_{n+1}(x)$. What seems to be happening is that at each stage, the numerator is picking up an additional factor that is equal to the previous denominator. So I would start by asking if $q_n(x)$, which I'll define to be the denominator of $p_n(x)$, has square discriminant. The first few $q_n(x)$ are irreducible in $\mathbb Q[x]$, so it's interesting that their discriminants are squares. | |
| Mar 27, 2018 at 20:06 | comment | added | Sylvain JULIEN | It seems judging from your list that for all $ n $ one has $ D_{n}\mid D_{n+1} $ . | |
| Mar 27, 2018 at 19:28 | history | edited | Joe Silverman | CC BY-SA 3.0 |
Improved formatting
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| Mar 27, 2018 at 19:14 | history | asked | Alexander Kalmynin | CC BY-SA 3.0 |