On real algebraic numbers in which the derivative of their minimal polynomial is small-Reference-Cited by-同舟云学术

On real algebraic numbers in which the derivative of their minimal polynomial is small

Published:2021-07-16 Issue:2 Volume:57 Page:135-147
ISSN:2524-2415
Container-title:Proceedings of the National Academy of Sciences of Belarus. Physics and Mathematics Series
language:
Short-container-title:Vescì Akademìì navuk Belarusì. Seryâ fizika-matematyčnyh navuk

Author:

Koleda D. V.¹

Affiliation:

1. Institute of Mathematics of the National Academy of Sciences of Belarus

Abstract

Algebraic numbers are the roots of integer polynomials. Each algebraic number α is characterized by its minimal polynomial Pα that is a polynomial of minimal positive degree with integer coprime coefficients, α being its root. The degree of α is the degree of this polynomial, and the height of α is the maximum of the absolute values of the coefficients of this polynomial. In this paper we consider the distribution of algebraic numbers α whose degree is fixed and height bounded by a growing parameter Q, and the minimal polynomial Pα is such that the absolute value of its derivative P'α (α) is bounded by a given parameter X. We show that if this bounding parameter X is from a certain range, then as Q → +∞ these algebraic numbers are distributed uniformly in the segment [-1+√2/3.1-√2/3]

Publisher

Publishing House Belorusskaya Nauka

Subject

Computational Theory and Mathematics,General Physics and Astronomy,General Mathematics

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