Open AccessOn distribution densities of algebraic points under different height functions
Author(s) -
Denis Koleda
Publication year - 2021
Publication title -
doklady nacionalʹnoj akademii nauk belarusi
Language(s) - English
Resource type - Journals
eISSN - 2524-2431
pISSN - 1561-8323
DOI - 10.29235/1561-8323-2021-65-6-647-653
Subject(s) - mathematics , degree (music) , distribution (mathematics) , polynomial , function (biology) , algebraic number , joint probability distribution , combinatorics , probability density function , upper and lower bounds , distribution function , mathematical analysis , statistics , physics , evolutionary biology , acoustics , biology , quantum mechanics
In the article we consider the spatial distribution of points, whose coordinates are conjugate algebraic numbers of fixed degree. The distribution is introduced using a height function. We have obtained universal upper and lower bounds of the distribution density of such points using an arbitrary height function. We have shown how from a given joint density function of coefficients of a random polynomial of degree n, one can construct such a height function H that the polynomials q of degree n uniformly chosen under H[q] ≤1 have the same distribution of zeros as the former random polynomial.