Correlations between real conjugate algebraic numbers
Friedrich G\"otze, Dzianis Kaliada, and Dmitry Zaporozhets

TL;DR
This paper derives an asymptotic formula for counting conjugate algebraic number tuples within a region, revealing their distribution and correlations as the height bound grows large.
Contribution
It provides an explicit asymptotic count and distribution density for conjugate algebraic numbers of degree up to n, including special cases for n=2.
Findings
Asymptotic formula for the number of conjugate algebraic tuples
Explicit density function for conjugate algebraic numbers
Additional logarithmic factor in the error term when n=2
Abstract
For denote by the number of ordered -tuples in of real conjugate algebraic numbers of degree and naive height . We show that where the function will be given explicitly. If , then an additional factor appears in the reminder term.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Analytic Number Theory Research · Advanced Algebra and Geometry
