danДоклады Национальной академии наук БеларусиDoklady of the National Academy of Sciences of Belarus1561-83232524-2431The Republican Unitary Enterprise Publishing House "Belaruskaya Navuka"10.29235/1561-8323-2021-65-5-519-525dan-999Research ArticleМАТЕМАТИКАMATHEMATICSОб алгебраических точках фиксированной степени и ограниченной высотыOn algebraic points of fixed degree and bounded heightКоледаД. В.KoledaD. V.

Коледа Денис Владимирович – канд. физ.-мат. наук, ст. науч. сотрудник

ул. Сурганова, 11, 220072, Минск

Koleda Denis V. – Ph. D. (Physics and Mathematics), Senior researcher

11, Surganov Str., 220072, Minsk

koledad@rambler.ruИнститут математики Национальной академии наук БеларусиInstitute of Mathematics of the National Academy of Sciences of Belarus202107112021655519–525Copyright © Коледа Д.В., 20212021Коледа Д.В.Koleda D.V.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://doklady.belnauka.by/jour/article/view/999

Рассматривается пространственное распределение точек с алгебраическими сопряженными координатами фиксированной степени и ограниченной высоты. В сообщении основной результат недавней работы автора с Ф. Гётце и Д. Н. Запорожцем распространен на случай произвольных высотных функций. Доказана асимптотическая формула для количества таких алгебраических точек, лежащих в заданной пространственной области. Получено явное выражение для плотности распределения алгебраических точек при произвольной высотной функции.

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.

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The authors declare that there are no conflicts of interest present.