文献类型：期刊文献

英文题名：MAHLER'S MEASURES ON FUNCTION SPACES

作者：Huang, Hansong

机构：[1]E China Univ Sci & Technol, Dept Math, Shanghai 200237, Peoples R China

年份：2011

卷号：55

期号：3

起止页码：1183

外文期刊名：ILLINOIS JOURNAL OF MATHEMATICS

收录：;WOS:【SCI-EXPANDED(收录号:WOS:000208745600021)】；

基金：Partially supported by NSFC (11001078), Shanghai Municipal Education Commission and Shanghai Education Development Foundation (11CG30), and Foundation of East China University of Science and Technology (yk0157118).

语种：英文

摘要：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).