2014/03/25 by David Krumm, Krumm, David
Computer Science · Mathematics · #Algebraic Geometry and Number Theory #Analytic Number Theory Research #Cryptography and Residue Arithmetic #FOS: Mathematics #Number Theory (math.NT) #Numerical Methods and Algorithms #math.NT
paper · pdf · doi:10.48550/arxiv.1403.6501
openalex publication_date 2014/03/25 · arxiv created 2014/08/02 · arxiv updated 2014/08/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We construct an algorithm for solving the following problem: given a number field K, a positive integer N, and a positive real number B, determine all points in \mathbb PN(K) having relative height at most B. A theoretical analysis of the efficiency of the algorithm is provided, as well as sample computations showing how the algorithm performs in practice. Two variants of the method are described, and examples are given to compare their running times. In the case N=1 we compare our method to an earlier algorithm for enumerating elements of bounded height in number fields.