Equilibrium points of logarithmic potentials on convex domains

dc.creatorLangley, J. K.
dc.date2006-01-30
dc.date.accessioned2026-07-07T06:59:28Z
dc.date.available2026-07-07T06:59:28Z
dc.descriptionLet $D$ be a convex domain in the plane. Let $a_k$ be summable positive constants and let each $z_k$ lie in $D$. If the $z_k$ converge sufficiently rapidly to a boundary point of $D$ from within an appropriate Stolz angle then the function $f(z) = \sum_{k=1}^\infty a_k /(z - z_k)$ has infinitely many zeros in $D$. An example shows that the hypotheses on the $z_k$ are not redundant, and that two recently advanced conjectures are false.
dc.identifierhttps://arxiv.org/abs/math/0601729
dc.identifierhttp://arxiv.org/abs/math/0601729
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/107759
dc.subjectComplex Variables
dc.subject30D35
dc.titleEquilibrium points of logarithmic potentials on convex domains
dc.typetext

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