Pisot unit generators in number fields. (November 2018)

• Record Type: Journal Article
• Authors: Vávra, T.; Veneziano, F.
• Is Part Of: Journal of symbolic computation. Volume 89(2018)
• Page Start: 94
• Page End: 108
• Publication Date: 2018-11
• Subjects: Pisot numbers -- Salem numbers -- Algebraic units; Mathematics -- Data processing -- Periodicals; Numerical analysis -- Data processing -- Periodicals; Automatic programming (Computer science) -- Periodicals; Mathématiques -- Informatique -- Périodiques; Analyse numérique -- Informatique -- Périodiques; Programmation automatique -- Périodiques; Automatic programming (Computer science); Mathematics -- Data processing; Numerical analysis -- Data processing; Periodicals; Electronic journals; 510.285
• DOI: 10.1016/j.jsc.2017.11.005
• Languages: English
• ISSNs: 0747-7171

Abstract

Abstract: Pisot numbers are real algebraic integers bigger than 1, whose other conjugates all have modulus smaller than 1. In this paper we deal with the algorithmic problem of finding the smallest Pisot unit generating a given number field. We first solve this problem in all real fields, then we consider the analogous problem involving the so called complex Pisot numbers and we solve it in all number fields that admit such a generator, in particular this includes all fields without CM.