Asymptotic zero distribution conjecture for Gonchar polynomials of the third kind
Asymptotic zero distribution conjecture for Gonchar polynomials of the third kind
Let be the set consisting of the boundary of the union of the two unit disks centered at and , together with the line segment connecting their intersection points. Let denote the Gonchar polynomial of the third kind in dimension with conical charge . Asymptotic zero distribution conjecture. As , all zeros of tend to , and every point of attracts zeros of these polynomials. This conjectural description identifies the limiting zero set for the Gonchar polynomials of the third kind; the supplied text does not indicate whether it has been proved or remains open.
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Primary source
Johann S. Brauchart, Peter D. Dragnev and Edward B. Saff, “An Electrostatics Problem on the Sphere Arising from a Nearby Point Charge”, arXiv:1402.3367 (2014).
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