The authors extend Pólya's shire theorem to hyperexponential functions f=(P/Q)exp(S/T), showing that normalized zero-counting measures of derivatives converge to a Voronoi edge measure augmented by weighted atoms at essential singularities, with explicit microscopic cluster laws.
Title resolution pending
2 Pith papers cite this work. Polarity classification is still indexing.
2
Pith papers citing it
fields
math.CV 2years
2026 2verdicts
UNVERDICTED 2representative citing papers
Zero-counting measures of P(D)^n applied to rational h with simple poles converge vaguely to [m(b-1)/(bm-r)] times the Bøgvad-Hägg measure on the Voronoi diagram of the poles, with a proportion of zeros escaping to infinity unless P is a pure derivative.
citing papers explorer
-
Zero asymptotics for successive derivatives of hyperexponential functions with finite essential singularities
The authors extend Pólya's shire theorem to hyperexponential functions f=(P/Q)exp(S/T), showing that normalized zero-counting measures of derivatives converge to a Voronoi edge measure augmented by weighted atoms at essential singularities, with explicit microscopic cluster laws.
-
Voronoi limit measures for iterates of constant-coefficient differential operators on rational functions with simple poles
Zero-counting measures of P(D)^n applied to rational h with simple poles converge vaguely to [m(b-1)/(bm-r)] times the Bøgvad-Hägg measure on the Voronoi diagram of the poles, with a proportion of zeros escaping to infinity unless P is a pure derivative.