Illinois Journal of Mathematics

An areal analog of Mahler’s measure

Igor E. Pritsker

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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

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

First available in Project Euclid: 23 July 2009

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Zentralblatt MATH identifier

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


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

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