Sasaki, Yoshikatsu Value distribution of the third Painlevé transcendents in sectorial domains. (English) Zbl 1152.34396 Proc. Japan Acad., Ser. A 83, No. 6, 79-82 (2007). Summary: This article concerns the value distribution of the third Painlevé transcendents in sectorial domains around fixed singular points. We show that the cardinality of the zeros of a third Painlevé transcendent in a sector has an asymptotic growth of finite order, thereby giving an improvement of the known estimation. Cited in 2 Documents MSC: 34M55 Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies 30D35 Value distribution of meromorphic functions of one complex variable, Nevanlinna theory 32A22 Nevanlinna theory; growth estimates; other inequalities of several complex variables × Cite Format Result Cite Review PDF Full Text: DOI References: [1] Y. Sasaki, Value distribution of the fifth Painlevé transcendents in sectorial domains, J. Math. Anal. Appl. 330 (2007), 817-828. · Zbl 1133.34049 · doi:10.1016/j.jmaa.2006.07.083 [2] Y. Sasaki, Construction of the auxiliary functions for the value distribution of the fifth Painlevé transcendents in sectorial domains, RIMS Kôkyûroku Bessatsu B2 (2007), 209-214. · Zbl 1132.34336 [3] S. Shimomura, Growth of modified Painlevé transcendents of the fifth and the third kind, Forum Math. 16 (2004), 231-247. · Zbl 1058.34127 · doi:10.1515/form.2004.011 [4] S. Shimomura, Value distribution of Painlevé transcendents of the third kind, Complex Variables Theory Appl. 40 (1999), no. 1, 51-62. · Zbl 1036.34108 [5] H. Umemura and H. Watanabe, Solutions of the third Painlevé equation. I, Nagoya Math. J. 151 (1998), 1-24. · Zbl 0917.34004 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.