On the discriminant of the power of an algebraic number

Author:

Dubickas Artūras1

Affiliation:

1. 1 Vilnius University Department of Mathematics and Informatics Naugarduko 24 Vilnius 03225 Lithuania

Abstract

Let α be an algebraic number which is not a root of a rational number. We show that the discriminant of αn tends to infinity with n tending to infinity and give a lower bound for this discriminant in terms of the degree of α , its Mahler’s measure and n .

Publisher

Akademiai Kiado Zrt.

Subject

General Mathematics

Reference12 articles.

1. Bell, J. P. and Hare, K. G. , Properties of Z -modules of algebraic numbers, (submitted).

2. On a question of Lehmer and the number of irreducible factors of a polynomial;Dobrowolski E.;Acta Arith.,1979

3. On subfields of a field generated by two conjugate algebraic numbers;Drungilas P.;Proc. Edinburgh Math. Soc.,2004

4. On the Remak height, the Mahler measure and conjugate sets of algebraic numbers lying on two circles;Dubickas A.;Proc. Edinburgh Math. Soc.,2001

Cited by 2 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Many Variations of Mahler Measures;AUST MATH SOC LECT;2020-05-07

2. On the Discriminants of the Powers of an Algebraic Integer;Canadian Mathematical Bulletin;2019-05-22

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