On distribution densities of algebraic points under different height functions
https://doi.org/10.29235/1561-8323-2021-65-6-647-653
Abstract
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.
About the Author
D. V. Koleda
Institute of Mathematics of the National Academy of Sciences of Belarus
Belarus
Belarus
Koleda Denis V. – Ph. D. (Physics and Mathematics), Senior researcher
11, Surganov Str., 220072, Minsk, Republic of Belarus
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