Illinois Journal of Mathematics

An areal analog of Mahler’s measure

Igor E. Pritsker

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Abstract

We consider a version of height on polynomial spaces defined by the integral over the normalized area measure on the unit disk. This natural analog of Mahler’s measure arises in connection with extremal problems for Bergman spaces. It inherits many nice properties such as the multiplicative one. However, this height is a lower bound for Mahler’s measure, and it can be substantially lower. We discuss some similarities and differences between the two.

Article information

Source
Illinois J. Math., Volume 52, Number 2 (2008), 347-363.

Dates
First available in Project Euclid: 23 July 2009

Permanent link to this document
https://projecteuclid.org/euclid.ijm/1248355339

Digital Object Identifier
doi:10.1215/ijm/1248355339

Mathematical Reviews number (MathSciNet)
MR2524641

Zentralblatt MATH identifier
1232.11111

Subjects
Primary: 11C08: Polynomials [See also 13F20]
Secondary: 11G50: Heights [See also 14G40, 37P30] 30C10: Polynomials

Citation

Pritsker, Igor E. An areal analog of Mahler’s measure. Illinois J. Math. 52 (2008), no. 2, 347--363. doi:10.1215/ijm/1248355339. https://projecteuclid.org/euclid.ijm/1248355339


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