Functiones et Approximatio Commentarii Mathematici

On the reduced length of a polynomial with real coefficients, II

Andrzej Schinzel

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Abstract

The length $L(P)$ of a polynomial $P$ is the sum of the absolute values of the coefficients. For $P\in\mathbb{R}[x]$ the properties of $l(P)$ are studied, where $l(P)$ is the infimum of $L(PG)$ for $G$ running through monic polynomials over $\mathbb{R}$.

Article information

Source
Funct. Approx. Comment. Math., Volume 37, Number 2 (2007), 445-459.

Dates
First available in Project Euclid: 18 December 2008

Permanent link to this document
https://projecteuclid.org/euclid.facm/1229619664

Digital Object Identifier
doi:10.7169/facm/1229619664

Mathematical Reviews number (MathSciNet)
MR2363837

Zentralblatt MATH identifier
1211.12003

Subjects
Primary: 12D99: None of the above, but in this section
Secondary: 26C99: None of the above, but in this section

Keywords
length of a polynomial unit circle

Citation

Schinzel, Andrzej. On the reduced length of a polynomial with real coefficients, II. Funct. Approx. Comment. Math. 37 (2007), no. 2, 445--459. doi:10.7169/facm/1229619664. https://projecteuclid.org/euclid.facm/1229619664


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References

  • A. Dubickas, Arithmetical properties of powers of algebraic numbers, Bull. London Math. Soc., 38 (2006), 70--80.
  • A. Schinzel, On the reduced length of a polynomial with real coefficients, Funct. Approx. Comment. Math. 35 (2006), 271--306.
  • A. Schinzel, On the reduced length of a polynomial with real coefficients, in: A. Schinzel, Selecta, vol. 1, 658--691.