5 papers
The full shadow of a polynomial I. The limiting core and the transient set
Christian Hägg, Boris Shapiro
The full shadow of a complex polynomial of degree is the closure of all zeros of , , . We prove that it consists of a compact connected l…
A Bézout domain that is not an elementary divisor domain
Christian Hägg, Anders Mörtberg
We settle in the negative the longstanding question whether every Bézout domain is an elementary divisor domain by constructing a Bézout domain over which an explicit m…
Zero asymptotics for successive derivatives of hyperexponential functions with finite essential singularities
Christian Hägg, Boris Shapiro
Pólya's shire theorem identifies the final set of zeros of successive derivatives of an arbitrary meromorphic function with at least one pole with the Voronoi diagram of its finite…
Voronoi limit measures for iterates of constant-coefficient differential operators on rational functions with simple poles
Bosco Nyandwi, Christian Hägg, Celestin Kurujyibwami +1
Bøgvad and Hägg proved that for a rational function with simple poles, the zeros of successive derivatives accumulate on the Voronoi diagram of the pole set, and the normalized zer…
The asymptotic zero-counting measure of iterated derivaties of a class of meromorphic functions
Christian Hägg
We give an explicit formula for the logarithmic potential of the asymptotic zero-counting measure of the sequence $\left\{\frac{\mathrm{d}^n}{\mathrm{d}z^n}\left(R(z)\exp{T(z)}\rig…