Equilibrium points of logarithmic potentials on convex domains
| dc.creator | Langley, J. K. | |
| dc.date | 2006-01-30 | |
| dc.date.accessioned | 2026-07-07T06:59:28Z | |
| dc.date.available | 2026-07-07T06:59:28Z | |
| dc.description | Let $D$ 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.identifier | https://arxiv.org/abs/math/0601729 | |
| dc.identifier | http://arxiv.org/abs/math/0601729 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/107759 | |
| dc.subject | Complex Variables | |
| dc.subject | 30D35 | |
| dc.title | Equilibrium points of logarithmic potentials on convex domains | |
| dc.type | text |