LOWER BOUNDS FOR MAHLER-TYPE MEASURES OF POLYNOMIALS

被引：0

作者：

Dubickas, Arturas ^{[1
]}

Pritsker, Igor ^{[2
]}

机构：

[1] Vilnius Univ, Inst Math, Fac Math & Informat, Naugarduko 24, LT-03225 Vilnius, Lithuania

[2] Oklahoma State Univ, Dept Math, Stillwater, OK 74078 USA

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2023年 / 151卷 / 09期

关键词：

Mahler measure; lower bound; sharp inequality; INTEGRAL-INEQUALITIES; SHARP INEQUALITIES;

D O I：

10.1090/proc/16381

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

. In this note we consider various generalizations of the classical Mahler measure M(P) = exp 0 log |P(ei theta) d theta for complex polynomials P, and prove sharp lower bounds for them. For example, we show that for any monic polynomial P is an element of C[z] satisfying |P (0)| = 1 the quantity M0 (P) = exp 0 max(0, log |P(ei theta)|) d theta is greater than or equal to M(1 + z1 + z2) = 1.381356.. .. This inequality is best possible, with equality being attained for all P(z) = zn + c with n is an element of N and |c| = 1.

引用

页码：3673 / 3680

页数：8

共 19 条

[1] Algebraic numbers close to 1 and variants of Mahler's measure [J].