A note on the quality of simultaneous Diophantine approximations obtained by the LLL algorithm
Number Theory
2023-10-04 v1
Abstract
In 1982, A. K. Lenstra, H. W. Lenstra, and L. Lov\'asz introduced the first polynomial-time method to factor a nonzero polynomial into irreducible factors. This algorithm, now commonly referred to as the LLL Algorithm, can also be applied to compute simultaneous Diophantine approximations. We present a significant improvement of a result by Bosma and Smeets on the quality of simultaneous Diophantine approximations achieved by the LLL Algorithm.
Cite
@article{arxiv.2310.01561,
title = {A note on the quality of simultaneous Diophantine approximations obtained by the LLL algorithm},
author = {Machiel van Frankenhuijsen and Edward K. Voskanian},
journal= {arXiv preprint arXiv:2310.01561},
year = {2023}
}
Comments
6 pages