2019/12/18 by Francesco Battistoni, Battistoni, Francesco
Computer Science · Mathematics · #Analytic Number Theory Research #Coding theory and cryptography #Cryptography and Residue Arithmetic #FOS: Mathematics #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.1912.08512
openalex publication_date 2019/12/18 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28
An inequality proved firstly by Remak and then generalized by Friedman shows\nthat there are only finitely many number fields with a fixed signature and\nwhose regulator is less than a prescribed bound. Using this inequality,\nAstudillo, Diaz y Diaz, Friedman and Ramirez-Raposo succeeded to detect all\nfields with small regulators having degree less or equal than 7. In this paper\nwe show that a certain upper bound for a suitable polynomial, if true, can\nimprove Remak-Friedman's inequality and allows a classification for some\nsignatures in degree 8 and better results in degree 5 and 7. The validity of\nthe conjectured upper bound is extensively discussed.\n