Some isoperimetric inequalities and their application to problems on polynomials

被引：0
作者：
V. Bentkus
A. Dubickas
机构：
[1] Institute of Mathematics and Informatics, 2600 Vilnius
[2] Department of Mathematics and Informatics, Vilnius University, 2600 Vilnius
来源：
Analysis Mathematica | 2003年 / 29卷 / 4期
关键词：
Linear Combination; Algebraic Number; Isoperimetric Inequality; Nondecreasing Function; Sharp Inequality;
D O I：
10.1023/B:ANAM.0000005369.36336.8e
中图分类号：
学科分类号：
摘要：
We prove sharp inequalities for the product of the Lebesgue integral of certain power of a positive absolutely continuous and nondecreasing function (or a linear combination of such distinct powers) and the Lebesgue integral of the square of its derivative. These inequalities are related to some problems for polynomials having small Mahler measure. As an application, we give a lower bound for the logarithmic height of a noncyclotomic algebraic number in terms of its degree. © 2003 Kluwer Academic Publisher/Akadémiai Kiadó.
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页码：259 / 279
页数：20
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