Timeline for In which cyclic cubic number fields does there exist this type of unit?
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
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| Nov 4, 2018 at 17:20 | comment | added | GNiklasch | @ChristineMcMeekin Depending on how formal you want it to be, "MO user GNiklasch" or "Gerhard Niklasch" or a reference along the lines of this or this other prior advice on MO meta. I've been out of academia for two decades, so I personally no longer care about citation counts: whichever variant fits the journal style and looks best to you (and your referee)! | |
| Nov 4, 2018 at 13:06 | comment | added | Christine McMeekin | GNiklasch, I'd like to mention you in the acknowledgements of a paper. To whom do I owe credit? | |
| Oct 11, 2018 at 14:40 | history | edited | GNiklasch | CC BY-SA 4.0 |
added more about congruence obstructions and references for same
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| Oct 9, 2018 at 19:01 | history | edited | GNiklasch | CC BY-SA 4.0 |
Expanding on question 2
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| Oct 9, 2018 at 16:51 | comment | added | GNiklasch | Fixed the wrong sign (thanks for pointing it out!).- Given a number field by a defining polynomial, it is always possible (at least in principle) to compute the set of all solutions to the unit equation $x+y=1$ in $\mathcal{O}_K^\times$, also known (following Nagell) as the set of exceptional units of $K$; in the cubic case it can be done "the wrong way round" by reducing to a Thue equation (even though computer algebra systems might internally reduce the Thue equation to an ($S$-)unit equation). | |
| Oct 9, 2018 at 16:40 | history | edited | GNiklasch | CC BY-SA 4.0 |
sign fixed
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| Oct 9, 2018 at 16:10 | comment | added | Christine McMeekin | Regarding your response to question 3, I think you mean $t^3+at^2−(a+3)t+1$. I've basically already done this except backwards; the code I wrote starts with $f$ and then computes $a$ instead of the other way around. If $a$ turns out to be an integer then I know $K$ is green, but if not then I'm not sure I can say whether $K$ is green or not. My code uses ideas from ``On Cyclic Cubic Fields" by Ennola and Turunen. I will continue to think about this. | |
| Oct 9, 2018 at 15:23 | comment | added | Christine McMeekin | Thanks! Perhaps then in the density question, I should consider only those cyclic cubic number fields in which 2 is inert/Q. From the LMFDB, I computed that f is green for at least 89 of the 810 conductors st. 2 is inert in K, cyclic cubic of conductor f. | |
| Oct 9, 2018 at 14:41 | history | answered | GNiklasch | CC BY-SA 4.0 |