Hostname: page-component-586b7cd67f-vdxz6 Total loading time: 0 Render date: 2024-12-04T09:15:07.589Z Has data issue: false hasContentIssue false
  • English
  • Français

ESTIMATES FOR MAHLER’S MEASURE OF A LINEAR FORM

Published online by Cambridge University Press:  01 July 2004

Fernando Rodriguez-Villegas ,
Ricardo Toledano  and
Jeffrey D. Vaaler
Fernando Rodriguez-Villegas
Affiliation:
Department of Mathematics, University of Texas, Austin, TX 78712, USA ([email protected]; [email protected])
Ricardo Toledano
Affiliation:
Instituto de Matematica y Fisica, Universidad de Talca, 2 Norte 685, Talca, Chile ([email protected])
Jeffrey D. Vaaler
Affiliation:
Department of Mathematics, University of Texas, Austin, TX 78712, USA ([email protected]; [email protected])
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Let $L_{\bm{a}}(\bm{z})=a_1z_1+a_2z_2+\cdots+a_Nz_N$ be a linear form in $N$ complex variables $z_1,z_2,\dots,z_N$ with non-zero coefficients. We establish several estimates for the logarithmic Mahler measure of $L_{\bm{a}}$. In general, we show that the logarithmic Mahler measure of $L_{\bm{a}}(\bm{z})$ and the logarithm of the norm of $\bm{a}$ differ by a bounded amount that is independent of $N$. We prove a further estimate which is useful for making an approximate numerical evaluation of the logarithmic Mahler measure.

AMS 2000 Mathematics subject classification: Primary 11C08; 11Y35; 26D15

Keywords

Mahler measurelinear formapproximation
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 47 , Issue 2 , June 2004 , pp. 473 - 494
Copyright
Copyright © Edinburgh Mathematical Society 2004