Remarks on results by Müger and Tuset on the moments of polynomials

Greg Markowsky, Dylan Phung

Research output: Contribution to journalArticleResearchpeer-review

Abstract

Let f(x) be a non-zero polynomial with complex coefficients, and Mp=∫01f(x)pdx for p a positive integer. In a recent paper, Müger and Tuset showed that lim supp→∞|Mp|1∕p>0, and conjectured that this limit is equal to the maximum amongst the critical values of f together with the values |f(0)| and |f(1)|. We give an example that shows that this conjecture is false. It also may be natural to guess that lim supp→∞|Mp|1∕p is equal to the maximum of |f(x)| on [0,1]. However, we give a counterexample to this as well. We also provide a few more guesses as to the behavior of the quantity lim supp→∞|Mp|1∕p.

Original languageEnglish
Pages (from-to)394-397
Number of pages4
JournalIndagationes Mathematicae
Volume32
Issue number2
DOIs
Publication statusPublished - Apr 2021

Keywords

  • Complex analysis
  • Contour integration
  • Moments of polynomials

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