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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## Details

### 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

where * α* = *α*_{1}; and *α*_{2}, …, *α _{n}* 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

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## Cite this paper

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.