Experimental Mathematics

On the Absolute Trace of Polynomials Having All Zeros in a Sector

V. Flammang

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Abstract

Let $\alpha$ be an algebraic integer all of whose conjugates lie in a sector $ | \operatorname{arg {\ z | \leq \theta$} with $ 0 \leq \theta <90^\circ$. Using the method of explicit auxiliary functions, we compute the greatest lower bound $v(\theta)$ of the absolute trace of $\alpha$, for $\theta$ belonging to seven subintervals of $[0,90^\circ)$. The polynomials involved in the auxiliary functions are found by Wu's algorithm.

Article information

Source
Experiment. Math., Volume 17, Issue 4 (2008), 443-450.

Dates
First available in Project Euclid: 27 May 2009

Permanent link to this document
https://projecteuclid.org/euclid.em/1243429957

Mathematical Reviews number (MathSciNet)
MR2484428

Zentralblatt MATH identifier
1182.11050

Subjects
Primary: 11R04: Algebraic numbers; rings of algebraic integers 11Y40: Algebraic number theory computations 12D10: Polynomials: location of zeros (algebraic theorems) {For the analytic theory, see 26C10, 30C15}

Keywords
Algebraic integer trace explicit auxiliary functions integer transfinite diameter

Citation

Flammang, V. On the Absolute Trace of Polynomials Having All Zeros in a Sector. Experiment. Math. 17 (2008), no. 4, 443--450. https://projecteuclid.org/euclid.em/1243429957


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