Value distribution of the fifth Painlevé transcendents in sectorial domains

This article is concerned with a value distribution of the fifth Painlevé transcendents in sectorial domains around a fixed singular point. We show that the cardinality of the 1-points of a fifth Painlevé transcendent in a sector has an asymptotic growth of finite order, thereby giving an improvement of the known estimates. © 2006 Elsevier Inc. All rights reserved.