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 language | English |
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Pages (from-to) | 394-397 |
Number of pages | 4 |
Journal | Indagationes Mathematicae |
Volume | 32 |
Issue number | 2 |
DOIs | |
Publication status | Published - Apr 2021 |
Keywords
- Complex analysis
- Contour integration
- Moments of polynomials