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      On maximum modulus points and zero sets of entire functions of regular growth

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      Author(s)
      Ostrovskii I.
      Üreyen, A.E.
      Date
      2008
      Source Title
      Rocky Mountain Journal of Mathematics
      Print ISSN
      0035-7596
      Volume
      38
      Issue
      2
      Pages
      583 - 618
      Language
      English
      Type
      Article
      Item Usage Stats
      119
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      Abstract
      Let f be an entire function. We denote by R(w, f) the distance between a maximum modulus point w and the zero set of f. In a previous paper, the authors obtained asymptotical lower bounds for R(w, f) as |w| → ∞ for functions of finite positive order and regular growth. In this work we extend those results to functions of either zero or infinite order and show that our results are sharp in sense of order. Copyright © 2008 Rocky Mountain Mathematics Consortium.
      Keywords
      Entire function
      Order
      Proximate order
      Regular growth
      Zero set
      Permalink
      http://hdl.handle.net/11693/23122
      Published Version (Please cite this version)
      http://dx.doi.org/10.1216/RMJ-2008-38-2-583
      Collections
      • Department of Electrical and Electronics Engineering 3702
      • Department of Mathematics 653
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