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2008 On the Absolute Trace of Polynomials Having All Zeros in a Sector
V. Flammang
Experiment. Math. 17(4): 443-450 (2008).

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.

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V. Flammang. "On the Absolute Trace of Polynomials Having All Zeros in a Sector." Experiment. Math. 17 (4) 443 - 450, 2008.

Information

Published: 2008
First available in Project Euclid: 27 May 2009

zbMATH: 1182.11050
MathSciNet: MR2484428

Subjects:
Primary: 11R04 , 11Y40 , 12D10

Keywords: Algebraic integer , explicit auxiliary functions , integer transfinite diameter , Trace

Rights: Copyright © 2008 A K Peters, Ltd.

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