Timeline for Techniques for computing fundamental units in cubic extensions
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
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| Apr 22, 2011 at 4:43 | comment | added | KConrad | I should say in the previous comment that the absolute value of the discriminant of that field is 23. The actual discriminant is -23. | |
| Apr 22, 2011 at 1:07 | history | edited | KConrad | CC BY-SA 3.0 |
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| Apr 22, 2011 at 1:06 | comment | added | KConrad | dstt: One basic example where it seems to be impossible to make this method work (even with a modification like the one I use in the second example) is the cubic field Q(a) where a^3 - a - 1 = 0. This field has discriminant 23, which is less than 24, and thus it is hopeless to get an inequality of the form 4u^{3/n} + 24 < |disc(Q(a))| for any unit u > 1 and positive integer n at all. | |
| Apr 21, 2011 at 19:59 | comment | added | dstt | Thanks. This seems to cover most cases I can come up with. I'll also take a look at Voronoi's algorithm. | |
| Apr 21, 2011 at 10:50 | history | answered | KConrad | CC BY-SA 3.0 |