F. Gotze

activity

20072025

most citedOn the Asymptotic Spectrum of Products of Independent Random Matrices

56 citations · 199 across the 30 of their papers we have counts for

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math.NT2018

Distribution of complex algebraic numbers on the unit circle

Friedrich Götze, Anna Gusakova, Zakhar Kabluchko +1

For $- π \leq β_{1} < β_{2} \leq π$ denote by $Φ_{β_{1}, β_{2}} (Q)$ the number of algebraic numbers on the unit circle with arguments in $[β_{1}, β_{2}]$ of degree $2 m$ and with elliptic height at most…

math.NT2017

Joint distribution of conjugate algebraic numbers: a random polynomial approach

Friedrich Götze, Denis Koleda, Dmitry Zaporozhets

We count the algebraic numbers of fixed degree by their $w$ -weighted $l_{p}$ -norm which generalizes the naïve height, the length, the Euclidean and the Bombieri norms. For n…

math.NT2015★ 5 cited

Correlations between real conjugate algebraic numbers

Friedrich Götze, Dzianis Kaliada, Dmitry Zaporozhets

For $B \subset R^{k}$ denote by $Φ_{k} (Q; B)$ the number of ordered $k$ -tuples in $B$ of real conjugate algebraic numbers of degree $\leq n$ and naive height $\leq Q$ . We show th…

math.NT2010★ 3 cited

Distribution of Values of Quadratic Forms at Integral Points

Paul Buterus, Friedrich Götze, Thomas Hille +1

The number of lattice points in $d$ -dimensional hyperbolic or elliptic shells ${m : a < Q [m] < b}$ , which are restricted to rescaled and growing domains $r Ω$ , is approximated by th…