On some application of the spectral properties of the matrices

Aleksander Grytczuk and Izabela Kurzydło
Notes on Number Theory and Discrete Mathematics, ISSN 1310-5132
Volume 17, 2011, Number 2, Page 12—17
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Authors and affiliations

Aleksander Grytczuk
Faculty of Mathematics, Computer Science and Econometrics,
University of Zielona Gora,
65-516 Zielona Gora, Poland

Izabela Kurzydło
Faculty of Mathematics, Computer Science and Econometrics,
University of Zielona Gora,
65-516 Zielona Gora, Poland

Abstract

In the paper [14] A. Schinzel and H. Zassenhaus posed the following conjecture: If α ≠ 0 is an algebraic integer of degree n which is not a root of unity, then there exists a constant c > 0 such that
\left\vert \overline{\alpha }\right\vert \geq 1+\frac{c}{n},\text{ where } \left\vert \overline{\alpha }\right\vert =\max_{1\leq \text{ }i\text{ }\leq n}|\alpha _{i}|,
where α = α1; and α2, …, αn are the conjugates of α.
In this paper we give some information concerning this conjecture. In the proofs of the theorems we use some spectral properties of matrices.

Keywords

  • Conjecture of A. Schinzel and H. Zassenhaus
  • Spectral properties of matrices

AMS Classification

  • 11R04
  • 15A42

References

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Cite this paper

APA

Grytczuk, A., & Kurzydło, I. (2011). On some application of the spectral properties of the matrices. Notes on Number Theory and Discrete Mathematics, 17(2), 12-17.

Chicago

Grytczuk, Aleksander, and Izabela Kurzydło. “On Some Application of the Spectral Properties of the Matrices.” Notes on Number Theory and Discrete Mathematics 17, no. 2 (2011): 12-17.

MLA

Grytczuk, Aleksander, and Izabela Kurzydło. “On Some Application of the Spectral Properties of the Matrices.” Notes on Number Theory and Discrete Mathematics 17.2 (2011): 12-17. Print.

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