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

Zhijie Chen; Ting Jung Kuo; Chang Shou Lin

doi:10.1007/s11425-018-9355-0

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

Zhijie Chen, Ting Jung Kuo, Chang Shou Lin^*

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

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 language	English
Pages (from-to)	2089-2102
Number of pages	14
Journal	Science China Mathematics
Volume	62
Issue number	11
DOIs	https://doi.org/10.1007/s11425-018-9355-0
Publication status	Published - 2019 Nov 1

Keywords

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

ASJC Scopus subject areas

General Mathematics

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10.1007/s11425-018-9355-0

Cite this

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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 Painlev{\'e} 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.",

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N2 - 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.

AB - 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.

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KW - Green function

KW - Painlevé VI equation

KW - simple zero property

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

Abstract

Keywords

ASJC Scopus subject areas

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