Moments of polynomials with random multiplicative coefficients

Jacques Benatar, Alon Nishry, Brad Rodgers*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

5 Scopus citations

Abstract

For (Formula presented.) a Rademacher or Steinhaus random multiplicative function, we consider the random polynomials (Formula presented.) and show that the (Formula presented.) th moments on the unit circle (Formula presented.) tend to Gaussian moments in the sense of mean-square convergence, uniformly for (Formula presented.), but that in contrast to the case of independent and identically distributed coefficients, this behavior does not persist for (Formula presented.) much larger. We use these estimates to (i) give a proof of an almost sure Salem–Zygmund type central limit theorem for (Formula presented.), previously obtained in unpublished work of Harper by different methods, and (ii) show that asymptotically almost surely (Formula presented.) for all (Formula presented.).

Original languageEnglish
Pages (from-to)191-216
Number of pages26
JournalMathematika
Volume68
Issue number1
DOIs
StatePublished - Jan 2022

Funding

FundersFunder number
National Science Foundation1854398
Horizon 2020 Framework Programme692616
Natural Sciences and Engineering Research Council of Canada
European Research Council
Israel Science Foundation1903/18

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