2023/10/02 by Machiel van Frankenhuijsen, van Frankenhuijsen, Machiel, Edward K. Voskanian +1
Computer Science · Mathematics · #11J99 #Algebraic Geometry and Number Theory #FOS: Mathematics #Mathematical Dynamics and Fractals #Number Theory (math.NT) #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.2310.01561
openalex publication_date 2023/10/02 · openalex created_date 2023/10/05 · openalex updated_date 2026/07/28
In 1982, A. K. Lenstra, H. W. Lenstra, and L. Lovász introduced the first polynomial-time method to factor a nonzero polynomial f ∈ 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.