D. Zaporozhets

activity

20112026

most citedAsymptotic distribution of complex zeros of random analytic functions

78 citations · 138 across the 27 of their papers we have counts for

collaborators

Showing math.NTShow all

5 papers · 1 filter

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.NT2014

Distribution of complex algebraic numbers

Friedrich Götze, Dzianis Kaliada, Dmitry Zaporozhets

For a region $Ω \subset C$ denote by $Ψ (Q; Ω)$ the number of complex algebraic numbers in $Ω$ of degree $\leq n$ and naive height $\leq Q$ . We show that $$ Ψ(Q;Ω)=\frac{Q^{n+…

math.NT2014★ 4 cited

Discriminant and root separation of integral polynomials

Friedrich Götze, Dmitry Zaporozhets

Consider a random polynomial $G_{Q} (x) = ξ_{Q, n} x^{n} + ξ_{Q, n - 1} x^{n - 1} + ... + ξ_{Q, 0}$ with independent coefficients uniformly distributed on $2 Q + 1$ integer points ${- Q, ..., Q}$ . Den…