Mathematics – Number Theory
Scientific paper
2010-01-23
Mathematics
Number Theory
14 pages, 4 figures
Scientific paper
We present an algorithm that unconditionally computes a representation of the unit group of a number field of discriminant $\Delta_K$, given a full-rank subgroup as input, in asymptotically fewer bit operations than the baby-step giant-step algorithm. If the input is assumed to represent the full unit group, for example, under the assumption of the Generalized Riemann Hypothesis, then our algorithm can unconditionally certify its correctness in expected time $O(\Delta_K^{n/(4n + 2) + \epsilon}) = O(\Delta_K^{1/4 - 1/(8n+4) + \epsilon})$ where $n$ is the unit rank.
Fontein Felix
Jacobson Michael J. Jr.
No associations
LandOfFree
Rigorous Computation of Fundamental Units in Algebraic Number Fields does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Rigorous Computation of Fundamental Units in Algebraic Number Fields, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Rigorous Computation of Fundamental Units in Algebraic Number Fields will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-515262