Timeline for In which cyclic cubic number fields does there exist this type of unit?
Current License: CC BY-SA 4.0
15 events
| when toggle format | what | by | license | comment | |
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| Oct 18, 2018 at 12:15 | answer | added | GNiklasch | timeline score: 1 | |
| Oct 13, 2018 at 19:19 | answer | added | Stanley Yao Xiao | timeline score: 2 | |
| Oct 13, 2018 at 16:30 | answer | added | Christine McMeekin | timeline score: 0 | |
| Oct 11, 2018 at 14:44 | comment | added | GNiklasch | @StanleyYaoXiao you can of course compute these for any given $f$, and then the fundamental units, and then the exceptional units if any - but not by a single universal formula where you'd just plug in $f$. | |
| Oct 10, 2018 at 21:01 | comment | added | Stanley Yao Xiao | Would knowing 1) an explicit binary cubic form which represents (the ring of integers of) $K$ and 2) (conjecturally) an explicit (ternary) norm form in terms of this binary cubic form, which implicitly gives a normalized basis help? | |
| Oct 10, 2018 at 10:59 | history | edited | Christine McMeekin | CC BY-SA 4.0 |
added 4 characters in body
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| Oct 9, 2018 at 19:42 | comment | added | KConrad | @GNiklasch I edited the definition of $G_N$ and $B_N$ to make that clearer in the notation. Not sure why you could not edit for that. | |
| Oct 9, 2018 at 19:41 | history | edited | KConrad | CC BY-SA 4.0 |
inserted "size" symbols to make it clearer than B_N and G_N are counting sizes and are not the sets themselves
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| Oct 9, 2018 at 17:05 | comment | added | GNiklasch | It almost goes without saying, but $G_N$ and $B_N$ are the cardinalities of the two sets. (Too few characters for me to edit...) | |
| Oct 9, 2018 at 16:41 | history | edited | Joe Silverman | CC BY-SA 4.0 |
Improved formatting
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| Oct 9, 2018 at 16:36 | comment | added | Joe Silverman | Nice question. I'm going to edit a bit to improve readability, hope that's okay. Also, I'm sure you're already aware, but there's been lots of work on $w\in\mathcal O_K$ such that $w$ and $1-w$ have norm 1, i.e., they're both units. Then $w$ is called an exceptional unit. So the $w$ in your blue case might be called very exceptional units! | |
| Oct 9, 2018 at 16:16 | comment | added | Christine McMeekin | After reading GNiklasch's comments, I think for the density question it may make more sense to restrict both $G_N$ and $B_N$ only to number fields in which 2 is inert/Q and then ask the limit of $G_N/B_N$ as $N\to\infty$. | |
| Oct 9, 2018 at 14:41 | answer | added | GNiklasch | timeline score: 14 | |
| Oct 9, 2018 at 12:46 | comment | added | Chris Wuthrich | +1 for the colourblind-friendly choice of colours. | |
| Oct 9, 2018 at 12:32 | history | asked | Christine McMeekin | CC BY-SA 4.0 |