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Trigonometric Sums and Their Applications pp 29–69Cite as

Recent Progress in the Study of Polynomials with Constrained Coefficients

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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.

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  1. Department of Mathematics, Texas A&M University, College Station, TX, USA

    Tamás Erdélyi

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  1. Moscow Institute of Physics and Technology, Dolgoprudny, Russia, Moscow state University, Moscow, Russia, Buryat State University, Ulan-Ude, Russia, Caucasus Mathematical Center, Adyghe State University, Maykop, Russia

    Andrei Raigorodskii

  2. Institute of Mathematics, University of Zurich, Zurich, Switzerland, Moscow Institute of Physics and Technology, Dolgoprudny, Russia, Institute for Advanced Study Program in Interdisciplinary Studies, Princeton, NJ, USA

    Michael Th. Rassias

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Erdélyi, T. (2020). Recent Progress in the Study of Polynomials with Constrained Coefficients. In: Raigorodskii, A., Rassias, M. (eds) Trigonometric Sums and Their Applications. Springer, Cham. https://doi.org/10.1007/978-3-030-37904-9_2

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