Open AccessOn algebraic points of fixed degree and bounded height
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 - 10.29235/1561-8323-2021-65-5-519-525
Subject(s) - mathematics , bounded function , algebraic number , algebraic expression , degree (music) , function (biology) , algebraic surface , singular point of an algebraic variety , combinatorics , mathematical analysis , physics , evolutionary biology , biology , acoustics , differential algebraic equation , ordinary differential equation , differential equation
We consider the spatial distribution of points, whose coordinates are conjugate algebraic numbers of fixed de- gree and bounded height. In the article the main result of a recent joint work by the author and F. Götze, and D. N. Zaporozhets is extended to the case of arbitrary height functions. We prove an asymptotic formula for the number of such algebraic points lying in a given spatial region. We obtain an explicit expression for the density function of algebraic points under an arbitrary height function.