2018/10/11 by Hairong Yi, Yi, Hairong, Chang Lv +1
Computer Science · Mathematics · #11Y40 #Algebraic Geometry and Number Theory #Analytic Number Theory Research #Coding theory and cryptography #FOS: Mathematics #Number Theory (math.NT) #Primary 11R37 #math.NT #msc:11R37 #msc:11Y40
paper · pdf · doi:10.48550/arxiv.1810.04810
arxiv created 2018/10/11 · openalex publication_date 2018/10/11 · arxiv updated 2018/10/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For a number field K, we extend the notion of the ring class field of an order in K [C. Lv and Y. Deng, SciChina. Math., 2015] to that of an arbitrary number ring in K. We give both ideal-theoretic and idele-theoretic description of this number ring class field, and characterize it as a subfield of the ring class field of some order. As an application, we use it to give a criterion of the solvability of a higher degree norm form equation over a number ring and finally describe algorithms to compute this field.