Hilbert transforms and the equidistribution of zeros of polynomials

Emanuel Carneiro, Mithun Kumar Das, Alexandra Florea, Angel V. Kumchev, Amita Malik, Micah B. Milinovich, Caroline Turnage-Butterbaugh, Jiuya Wang

Research output: Contribution to journalArticlepeer-review

8 Scopus citations

Abstract

We improve the current bounds for an inequality of Erdős and Turán from 1950 related to the discrepancy of angular equidistribution of the zeros of a given polynomial. Building upon a recent work of Soundararajan, we establish a novel connection between this inequality and an extremal problem in Fourier analysis involving the maxima of Hilbert transforms, for which we provide a complete solution. Prior to Soundararajan (2019), refinements of the discrepancy inequality of Erdős and Turán had been obtained by Ganelius (1954) and Mignotte (1992).

Original languageEnglish (US)
Article number109199
JournalJournal of Functional Analysis
Volume281
Issue number9
DOIs
StatePublished - Nov 1 2021

All Science Journal Classification (ASJC) codes

  • Analysis

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