Recent Progress in the Study of Polynomials with Constrained Coefficients

Tamás Erdélyi ()
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Tamás Erdélyi: Texas A&M University, Department of Mathematics

A chapter in Trigonometric Sums and Their Applications, 2020, pp 29-69 from Springer

Abstract: Abstract This survey gives a taste of the author’s recent work on polynomials with constrained coefficients. Special attention is paid to unimodular, Littlewood, Newman, Rudin-Shapiro, and Fekete polynomials, their flatness and ultraflatness properties, their L q norms on the unit circle including Mahler’s measure, and bounds on the number of unimodular zeros of self-reciprocal polynomials with coefficients from a finite set of real numbers. Some interesting connections are explored, and a few conjectures are also made.

Keywords: Unimodular; Littlewood; Newman; Rudin-Shapiro; Fekete; polynomials; L q norms; Mahler’s measure; Zeros; 11C08; 41A17; 26C10; 30C15 (search for similar items in EconPapers)
Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-030-37904-9_2

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DOI: 10.1007/978-3-030-37904-9_2

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