Removable Sets in the Oscillation Theory of Complex Differential Equations

  title={Removable Sets in the Oscillation Theory of Complex Differential Equations},
  author={Ilpo Laine and Shengjian Wu},
  journal={Journal of Mathematical Analysis and Applications},
  • I. LaineShengjian Wu
  • Published 1 October 1997
  • Mathematics, Philosophy
  • Journal of Mathematical Analysis and Applications
Abstract Letf1, f2be two linearly independent solutions of the linear differential equationf″ + A(z)f = 0, whereA(z) is transcendental entire, and assume that the exponents of convergence for the zero-sequences off1, f2satisfy max(λ(f1), λ(f2)) = ∞. Our main result proves that the zeros ofE ≔ f1f2are uniformly distributed in the sense that quite arbitrary large areas of the complex plane can be removed in such a way that if only zeros outside of these areas will be counted for the exponents of… 

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