On algebraic points of fixed degree and bounded height
https://doi.org/10.29235/1561-8323-2021-65-5-519-525
Abstract
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.
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
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