Equilibrium Points of Logarithmic Potentials on Convex Domains
نویسنده
چکیده
Let D be a convex domain in C. Let ak > 0 be summable constants and let zk ∈ D. If the zk converge sufficiently rapidly to η ∈ ∂D from within an appropriate Stolz angle then the function ∑ ∞ k=1 ak/(z − zk) has infinitely many zeros in D. An example shows that the hypotheses on the zk are not redundant, and that two recently advanced conjectures are false. M.S.C. 2000 classification: 30D35, 31A05, 31B05.
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