Machiel van Frankenhuijsen, Edward K. Voskanian
Published 2023-10-02Version 1
In 1982, A. K. Lenstra, H. W. Lenstra, and L. Lov\'asz introduced the first polynomial-time method to factor a nonzero polynomial $f \in \mathbb{Q}[x]$ 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.
An LLL algorithm with symmetries
LLL Algorithm for Lattice Basis Reduction
On simultaneous diophantine approximations to $ζ(2)$ and $ζ(3)$
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