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Fall 2011 Mahler’s measures on function spaces
Hansong Huang
Illinois J. Math. 55(3): 1183-1202 (Fall 2011). DOI: 10.1215/ijm/1369841802

Abstract

Recently, I. Pritsker considered a Bergman-space version of Mahler’s measure, and obtained many nice properties such as the arithmetic nature, relation with asymptotic zero distribution, etc. (Illinois J. Math. 52 (2009) 347–363). In this paper, we define a Fock-space analogue of Mahler’s measure, and show a similar version of Lehmer’s conjecture. Inspired by this result, we establish an equivalent form of Lehmer’s conjecture. Also, this consideration is done on weighted Bergman spaces. However, it is shown that in this case the corresponding form of Lehmer’s conjecture fails. In addition, we give an affirmative answer to an approximation question raised by I. Pritsker (Illinois J. Math. 52 (2009) 347–363).

Citation

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Hansong Huang. "Mahler’s measures on function spaces." Illinois J. Math. 55 (3) 1183 - 1202, Fall 2011. https://doi.org/10.1215/ijm/1369841802

Information

Published: Fall 2011
First available in Project Euclid: 29 May 2013

zbMATH: 1272.11114
MathSciNet: MR3069301
Digital Object Identifier: 10.1215/ijm/1369841802

Subjects:
Primary: 11L07, 26C99

Rights: Copyright © 2011 University of Illinois at Urbana-Champaign

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Vol.55 • No. 3 • Fall 2011
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