A selection from Stockholm University publication database

• The asymptotic zero-counting measure of iterated derivaties of a class of meromorphic functions

  2019. Christian Hägg. Arkiv för matematik 57 (1), 107-120

  Article

  We give an explicit formula for the logarithmic potential of the asymptotic zero-counting measure of the sequence {(d(n)/dz(n)) (R(z) expT(z))}(n=1)(infinity). Here, R(z) is a rational function with at least two poles, all of which are distinct, and T(z) is a polynomial. This is an extension of a recent measure-theoretic refinement of Polya's Shire theorem for rational functions.

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• A refinement for rational functions of Polya's method to construct Voronoi diagrams

  2017. Rikard Bögvad, Christian Hägg. Journal of Mathematical Analysis and Applications 452 (1), 312-334

  Article

  Given a complex polynomial P with zeroes z(1),..., z(d), we show that the asymptotic zero-counting measure of the iterated derivatives Q((n)), n = 1, 2,..., where Q = R/P is any irreducible rational function, converges to an explicitly constructed probability measure supported by the Voronoi diagram associated with z(1),...,z(d). This refines Polya's Shire theorem for these functions. In addition, we prove a similar result, using currents, for Voronoi diagrams associated with generic hyperplane configurations in C-m.

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