Timeline for Short basis for the unit group of a number field
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
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| May 8, 2013 at 22:22 | vote | accept | user27318 | ||
| May 4, 2013 at 21:09 | comment | added | Joe Silverman | @Asaf: Aren't real quadratic fields the 1-dimensional case? So your comments are probably more relevant to, say, a totally real cubic field. | |
| May 4, 2013 at 21:07 | answer | added | Joe Silverman | timeline score: 2 | |
| May 4, 2013 at 18:37 | comment | added | Asaf | Think about this in the 2-dim case (say real quad. fields). The "short" basis will be basically consists of the first and second shortest vectors. The "bound" your asking is for how high the point representing this lattice goes to the cusp in the homogeneous space PSL2(R)/PSL2(Z). As can be seen by the basic theory of quad. forms, you can get forms of very large discriminant which will result at point very high up in the cusp (that means the shortest vector is very short, hence in the 2-dim case, the second one is very long). In general I think you might get something from Baker's inequality. | |
| May 4, 2013 at 18:00 | history | asked | user27318 | CC BY-SA 3.0 |