Geodesic
Distribution of complex algebraic numbers on the unit circle
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 27, Tome 474 (2018), pp. 90-107 Cet article a éte moissonné depuis la source Math-Net.Ru

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For $-\pi\leq\beta_1<\beta_2\leq\pi$ denote by $\Phi_{\beta_1,\beta_2}(Q)$ the number of algebraic numbers on the unit circle with arguments in $[\beta_1,\beta_2]$ of degree $2m$ and with elliptic height at most $Q$. We show that $$ \Phi_{\beta_1,\beta_2}(Q)=Q^{m+1}\int\limits_{\beta_1}^{\beta_2}{p(t)}\,\mathrm{d}t+O\left(Q^m\,\log Q\right),\quad Q\to\infty, $$ where $p(t)$ coincides up to a constant factor with the density of the roots of some random trigonometric polynomial. This density is calculated explicitly using the Edelman–Kostlan formula. 
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F. Götze; A. Gusakova; Z. Kabluchko; D. Zaporozhets. Distribution of complex algebraic numbers on the unit circle. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 27, Tome 474 (2018), pp. 90-107. http://geodesic.mathdoc.fr/item/ZNSL_2018_474_a5/

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