@article{89570aa5c28c45a9b32a4fc734d94164,
title = "Simple zero property of some holomorphic functions on the moduli space of tori",
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.",
keywords = "34M35, 34M55, Green function, Painlev{\'e} VI equation, simple zero property",
author = "Zhijie Chen and Kuo, {Ting Jung} and Lin, {Chang Shou}",
note = "Publisher Copyright: {\textcopyright} 2019, Science China Press and Springer-Verlag GmbH Germany, part of Springer Nature.",
year = "2019",
month = nov,
day = "1",
doi = "10.1007/s11425-018-9355-0",
language = "English",
volume = "62",
pages = "2089--2102",
journal = "Science China Mathematics",
issn = "1674-7283",
publisher = "Science in China Press",
number = "11",
}