Equidistribution of Zeros of Polynomials

Equidistribution of Zeros of Polynomials

A classical result of Erdős and Turán states that if a monic polynomial has small size on the unit circle and its constant coefficient is not too small, then its zeros cluster near the unit circle and become equidistributed in angle. Using Fourier analysis we give a short and self-contained proof of...

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Veröffentlicht in:The American mathematical monthly 2019-03, Vol.126 (3), p.226-236
1. Verfasser: Soundararajan, K.
Format: Artikel
Sprache:eng
Schlagworte:
Fourier analysis
Mathematical analysis
Polynomials
Primary 42A05
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Zusammenfassung:A classical result of Erdős and Turán states that if a monic polynomial has small size on the unit circle and its constant coefficient is not too small, then its zeros cluster near the unit circle and become equidistributed in angle. Using Fourier analysis we give a short and self-contained proof of this result.
ISSN:0002-9890
1930-0972
DOI:10.1080/00029890.2019.1546078