Paucity phenomena for polynomial products

Victor Y. Wang, Max Wenqiang Xu

Type: Article

Publication Date: 2024-05-31

Citations: 1

DOI: https://doi.org/10.1112/blms.13095

Abstract

Abstract Let be a polynomial with at least two distinct complex roots. We prove that the number of solutions to the equation (for any ) is asymptotically as . This solves a question first proposed and studied by Najnudel. The result can also be interpreted as saying that all even moments of random partial sums match standard complex Gaussian moments as , where is the Steinhaus random multiplicative function.

Locations

Bulletin of the London Mathematical Society - View
arXiv (Cornell University) - View - PDF

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