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 2014Show all

4 papers · 1 filter

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.PR2014★ 78 cited

Asymptotic distribution of complex zeros of random analytic functions

Zakhar Kabluchko, Dmitry Zaporozhets

Let $ξ_{0}, ξ_{1}, \dots$ be independent identically distributed complex- valued random variables such that $E lo g (1 + ∣ ξ_{0} ∣) < \infty$ . We consider random analytic functions of th…

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…

math.PR2014

Intrinsic volumes of Sobolev balls with applications to Brownian convex hulls

Zakhar Kabluchko, Dmitry Zaporozhets

A formula due to Sudakov relates the first intrinsic volume of a convex set in a Hilbert space to the maximum of the isonormal Gaussian process over this set. Using this formula we…