The total distance for totally positive algebraic integers

Authors

  • V. Flammang Université de Lorraine, site de Metz, France

Keywords:

total distance, totally positive algebraic, auxiliary functions, recursive algorithm

Abstract

Let \(P(x)\) be a degree \(d\) polynomial with zeros \(a_1\), \(\ldots\), \(a_d\). Stulov and Yang [‘An elementary inequality about the Mahler measure’, Involve 6(4) (2013), 393–397] defined the total distance of \(P\) as \({\rm td}(P)=\sum_{i=1}^{d} | | a_i| -1|\). In this paper, using the method of explicit auxiliary functions, we study the spectrum of the total distance for totally positive algebraic integers and find its five smallest points. Moreover, for totally positive algebraic integers, we establish inequalities comparing the total distance with two standard measures. We give numerical examples to show that our bounds are quite good. The polynomials involved in the auxiliary functions are found by a recursive algorithm. DOI:- 10.1017/S0004972714000537

Published

2014-09-20

Issue

Vol. 90 No. 3 (2014)

Section

Articles
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