Frequency of a-points for the fifth and the third Painlevé transcendents in a sector

Shun Shimomura

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


For the fifth Painlevé transcendents in a sector, under the condition that the values taken along some curve tending to infinity are bounded away from 1 and another specified complex number, we present new upper estimates for the number of a-points including poles and for the growth order. As far as we are concerned with the known asymptotic solutions of the fifth Painlevé equation, this condition is easily checked, and our results are applicable to almost all of them. About concrete examples we discuss the frequency of a-points, the equi-distribution property and the growth order. Our method works on the third Painlevé transcendents as well, yielding an analogous result.

Original languageEnglish
Pages (from-to)591-605
Number of pages15
JournalTohoku Mathematical Journal
Issue number4
Publication statusPublished - 2013 Dec
Externally publishedYes


  • Asymptotic solution
  • Growth order
  • Painlevé equations
  • Value distribution

ASJC Scopus subject areas

  • Mathematics(all)


Dive into the research topics of 'Frequency of a-points for the fifth and the third Painlevé transcendents in a sector'. Together they form a unique fingerprint.

Cite this