Simple zero property of some holomorphic functions on the moduli space of tori

Zhijie Chen, Ting Jung Kuo, Chang Shou Lin

Research output: Contribution to journalArticle

Abstract

We prove that some holomorphic functions on the moduli space of tori have only simple zeros. Instead of computing the derivative with respect to the moduli parameter τ, we introduce a conceptual proof by applying Painlevé VI equation. As an application of this simple zero property, we obtain the smoothness of the degeneracy curves of trivial critical points for some multiple Green function.

Original languageEnglish
Pages (from-to)2089-2102
Number of pages14
JournalScience China Mathematics
Volume62
Issue number11
DOIs
Publication statusPublished - 2019 Nov 1

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Keywords

  • 34M35
  • 34M55
  • Green function
  • Painlevé VI equation
  • simple zero property

ASJC Scopus subject areas

  • Mathematics(all)

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